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C(x)\\,e^{-A(x)}",[572,1144,1146,1204],{"className":1145,"ariaHidden":646},[645],[572,1147,1149,1153,1195,1198,1201],{"className":1148},[650],[572,1150],{"className":1151,"style":1152},[654],"height:0.7167em;vertical-align:-0.2861em;",[572,1154,1156,1159],{"className":1155},[659],[572,1157,596],{"className":1158,"style":664},[659,663],[572,1160,1162],{"className":1161},[668],[572,1163,1165,1186],{"className":1164},[672,989],[572,1166,1168,1183],{"className":1167},[676],[572,1169,1172],{"className":1170,"style":1171},[680],"height:0.1514em;",[572,1173,1174,1177],{"style":999},[572,1175],{"className":1176,"style":689},[688],[572,1178,1180],{"className":1179},[693,694,695,696],[572,1181,564],{"className":1182},[659,663,696],[572,1184,1013],{"className":1185},[1012],[572,1187,1189],{"className":1188},[676],[572,1190,1193],{"className":1191,"style":1192},[680],"height:0.2861em;",[572,1194],{},[572,1196],{"className":1197,"style":746},[706],[572,1199,627],{"className":1200},[750],[572,1202],{"className":1203,"style":746},[706],[572,1205,1207,1211,1214,1217,1220,1223,1226],{"className":1206},[650],[572,1208],{"className":1209,"style":1210},[654],"height:1.138em;vertical-align:-0.25em;",[572,1212,942],{"className":1213,"style":1042},[659,663],[572,1215,612],{"className":1216},[728],[572,1218,615],{"className":1219},[659,663],[572,1221,618],{"className":1222},[735],[572,1224],{"className":1225,"style":739},[706],[572,1227,1229,1232],{"className":1228},[659],[572,1230,949],{"className":1231},[659,663],[572,1233,1235],{"className":1234},[668],[572,1236,1238],{"className":1237},[672],[572,1239,1241],{"className":1240},[676],[572,1242,1244],{"className":1243,"style":1038},[680],[572,1245,1246,1249],{"style":684},[572,1247],{"className":1248,"style":689},[688],[572,1250,1252],{"className":1251},[693,694,695,696],[572,1253,1255,1258,1261,1264,1267],{"className":1254},[659,696],[572,1256,954],{"className":1257},[659,696],[572,1259,957],{"className":1260},[659,663,696],[572,1262,612],{"className":1263},[728,696],[572,1265,615],{"className":1266},[659,663,696],[572,1268,618],{"className":1269},[735,696],[777,1271,1272,1273,1317,1318,1497,1498,1673,1674,1090],{},"Einsetzen. Die Terme mit ",[572,1274,1276,1296],{"className":1275},[575],[572,1277,1279],{"className":1278},[579],[581,1280,1281],{"xmlns":583},[585,1282,1283,1293],{},[588,1284,1285,1287,1289,1291],{},[594,1286,942],{},[598,1288,612],{"stretchy":611},[594,1290,615],{},[598,1292,618],{"stretchy":611},[638,1294,1295],{"encoding":640},"C(x)",[572,1297,1299],{"className":1298,"ariaHidden":646},[645],[572,1300,1302,1305,1308,1311,1314],{"className":1301},[650],[572,1303],{"className":1304,"style":721},[654],[572,1306,942],{"className":1307,"style":1042},[659,663],[572,1309,612],{"className":1310},[728],[572,1312,615],{"className":1313},[659,663],[572,1315,618],{"className":1316},[735]," heben sich weg, übrig bleibt ",[572,1319,1321,1373],{"className":1320},[575],[572,1322,1324],{"className":1323},[579],[581,1325,1326],{"xmlns":583},[585,1327,1328,1370],{},[588,1329,1330,1336,1338,1340,1342,1344,1360,1362,1364,1366,1368],{},[591,1331,1332,1334],{},[594,1333,942],{},[598,1335,602],{"mathvariant":600,"lspace":601,"rspace":601},[598,1337,612],{"stretchy":611},[594,1339,615],{},[598,1341,618],{"stretchy":611},[620,1343,622],{},[591,1345,1346,1348],{},[594,1347,949],{},[588,1349,1350,1352,1354,1356,1358],{},[598,1351,954],{},[594,1353,957],{},[598,1355,612],{"stretchy":611},[594,1357,615],{},[598,1359,618],{"stretchy":611},[598,1361,627],{},[594,1363,630],{},[598,1365,612],{"stretchy":611},[594,1367,615],{},[598,1369,618],{"stretchy":611},[638,1371,1372],{"encoding":640},"C'(x)\\,e^{-A(x)} = b(x)",[572,1374,1376,1479],{"className":1375,"ariaHidden":646},[645],[572,1377,1379,1382,1414,1417,1420,1423,1426,1470,1473,1476],{"className":1378},[650],[572,1380],{"className":1381,"style":1210},[654],[572,1383,1385,1388],{"className":1384},[659],[572,1386,942],{"className":1387,"style":1042},[659,663],[572,1389,1391],{"className":1390},[668],[572,1392,1394],{"className":1393},[672],[572,1395,1397],{"className":1396},[676],[572,1398,1400],{"className":1399,"style":681},[680],[572,1401,1402,1405],{"style":684},[572,1403],{"className":1404,"style":689},[688],[572,1406,1408],{"className":1407},[693,694,695,696],[572,1409,1411],{"className":1410},[659,696],[572,1412,602],{"className":1413},[659,696],[572,1415,612],{"className":1416},[728],[572,1418,615],{"className":1419},[659,663],[572,1421,618],{"className":1422},[735],[572,1424],{"className":1425,"style":739},[706],[572,1427,1429,1432],{"className":1428},[659],[572,1430,949],{"className":1431},[659,663],[572,1433,1435],{"className":1434},[668],[572,1436,1438],{"className":1437},[672],[572,1439,1441],{"className":1440},[676],[572,1442,1444],{"className":1443,"style":1038},[680],[572,1445,1446,1449],{"style":684},[572,1447],{"className":1448,"style":689},[688],[572,1450,1452],{"className":1451},[693,694,695,696],[572,1453,1455,1458,1461,1464,1467],{"className":1454},[659,696],[572,1456,954],{"className":1457},[659,696],[572,1459,957],{"className":1460},[659,663,696],[572,1462,612],{"className":1463},[728,696],[572,1465,615],{"className":1466},[659,663,696],[572,1468,618],{"className":1469},[735,696],[572,1471],{"className":1472,"style":746},[706],[572,1474,627],{"className":1475},[750],[572,1477],{"className":1478,"style":746},[706],[572,1480,1482,1485,1488,1491,1494],{"className":1481},[650],[572,1483],{"className":1484,"style":721},[654],[572,1486,630],{"className":1487},[659,663],[572,1489,612],{"className":1490},[728],[572,1492,615],{"className":1493},[659,663],[572,1495,618],{"className":1496},[735],", also ",[572,1499,1501,1551],{"className":1500},[575],[572,1502,1504],{"className":1503},[579],[581,1505,1506],{"xmlns":583},[585,1507,1508,1548],{},[588,1509,1510,1516,1518,1520,1522,1524,1526,1528,1530,1532,1534],{},[591,1511,1512,1514],{},[594,1513,942],{},[598,1515,602],{"mathvariant":600,"lspace":601,"rspace":601},[598,1517,612],{"stretchy":611},[594,1519,615],{},[598,1521,618],{"stretchy":611},[598,1523,627],{},[594,1525,630],{},[598,1527,612],{"stretchy":611},[594,1529,615],{},[598,1531,618],{"stretchy":611},[620,1533,622],{},[591,1535,1536,1538],{},[594,1537,949],{},[588,1539,1540,1542,1544,1546],{},[594,1541,957],{},[598,1543,612],{"stretchy":611},[594,1545,615],{},[598,1547,618],{"stretchy":611},[638,1549,1550],{"encoding":640},"C'(x) = b(x)\\,e^{A(x)}",[572,1552,1554,1611],{"className":1553,"ariaHidden":646},[645],[572,1555,1557,1561,1593,1596,1599,1602,1605,1608],{"className":1556},[650],[572,1558],{"className":1559,"style":1560},[654],"height:1.0019em;vertical-align:-0.25em;",[572,1562,1564,1567],{"className":1563},[659],[572,1565,942],{"className":1566,"style":1042},[659,663],[572,1568,1570],{"className":1569},[668],[572,1571,1573],{"className":1572},[672],[572,1574,1576],{"className":1575},[676],[572,1577,1579],{"className":1578,"style":681},[680],[572,1580,1581,1584],{"style":684},[572,1582],{"className":1583,"style":689},[688],[572,1585,1587],{"className":1586},[693,694,695,696],[572,1588,1590],{"className":1589},[659,696],[572,1591,602],{"className":1592},[659,696],[572,1594,612],{"className":1595},[728],[572,1597,615],{"className":1598},[659,663],[572,1600,618],{"className":1601},[735],[572,1603],{"className":1604,"style":746},[706],[572,1606,627],{"className":1607},[750],[572,1609],{"className":1610,"style":746},[706],[572,1612,1614,1617,1620,1623,1626,1629,1632],{"className":1613},[650],[572,1615],{"className":1616,"style":1210},[654],[572,1618,630],{"className":1619},[659,663],[572,1621,612],{"className":1622},[728],[572,1624,615],{"className":1625},[659,663],[572,1627,618],{"className":1628},[735],[572,1630],{"className":1631,"style":739},[706],[572,1633,1635,1638],{"className":1634},[659],[572,1636,949],{"className":1637},[659,663],[572,1639,1641],{"className":1640},[668],[572,1642,1644],{"className":1643},[672],[572,1645,1647],{"className":1646},[676],[572,1648,1650],{"className":1649,"style":1038},[680],[572,1651,1652,1655],{"style":684},[572,1653],{"className":1654,"style":689},[688],[572,1656,1658],{"className":1657},[693,694,695,696],[572,1659,1661,1664,1667,1670],{"className":1660},[659,696],[572,1662,957],{"className":1663},[659,663,696],[572,1665,612],{"className":1666},[728,696],[572,1668,615],{"className":1669},[659,663,696],[572,1671,618],{"className":1672},[735,696],". Integrieren liefert ",[572,1675,1677,1696],{"className":1676},[575],[572,1678,1680],{"className":1679},[579],[581,1681,1682],{"xmlns":583},[585,1683,1684,1694],{},[588,1685,1686,1688,1690,1692],{},[594,1687,942],{},[598,1689,612],{"stretchy":611},[594,1691,615],{},[598,1693,618],{"stretchy":611},[638,1695,1295],{"encoding":640},[572,1697,1699],{"className":1698,"ariaHidden":646},[645],[572,1700,1702,1705,1708,1711,1714],{"className":1701},[650],[572,1703],{"className":1704,"style":721},[654],[572,1706,942],{"className":1707,"style":1042},[659,663],[572,1709,612],{"className":1710},[728],[572,1712,615],{"className":1713},[659,663],[572,1715,618],{"className":1716},[735],[564,1718,1719,1720,1876],{},"Die allgemeine Lösung ist dann ",[572,1721,1723,1753],{"className":1722},[575],[572,1724,1726],{"className":1725},[579],[581,1727,1728],{"xmlns":583},[585,1729,1730,1750],{},[588,1731,1732,1734,1736,1742,1744],{},[594,1733,596],{},[598,1735,627],{},[931,1737,1738,1740],{},[594,1739,596],{},[594,1741,937],{},[598,1743,605],{},[931,1745,1746,1748],{},[594,1747,596],{},[594,1749,564],{},[638,1751,1752],{"encoding":640},"y = y_h + y_p",[572,1754,1756,1774,1830],{"className":1755,"ariaHidden":646},[645],[572,1757,1759,1762,1765,1768,1771],{"className":1758},[650],[572,1760],{"className":1761,"style":976},[654],[572,1763,596],{"className":1764,"style":664},[659,663],[572,1766],{"className":1767,"style":746},[706],[572,1769,627],{"className":1770},[750],[572,1772],{"className":1773,"style":746},[706],[572,1775,1777,1781,1821,1824,1827],{"className":1776},[650],[572,1778],{"className":1779,"style":1780},[654],"height:0.7778em;vertical-align:-0.1944em;",[572,1782,1784,1787],{"className":1783},[659],[572,1785,596],{"className":1786,"style":664},[659,663],[572,1788,1790],{"className":1789},[668],[572,1791,1793,1813],{"className":1792},[672,989],[572,1794,1796,1810],{"className":1795},[676],[572,1797,1799],{"className":1798,"style":996},[680],[572,1800,1801,1804],{"style":999},[572,1802],{"className":1803,"style":689},[688],[572,1805,1807],{"className":1806},[693,694,695,696],[572,1808,937],{"className":1809},[659,663,696],[572,1811,1013],{"className":1812},[1012],[572,1814,1816],{"className":1815},[676],[572,1817,1819],{"className":1818,"style":1020},[680],[572,1820],{},[572,1822],{"className":1823,"style":707},[706],[572,1825,605],{"className":1826},[711],[572,1828],{"className":1829,"style":707},[706],[572,1831,1833,1836],{"className":1832},[650],[572,1834],{"className":1835,"style":1152},[654],[572,1837,1839,1842],{"className":1838},[659],[572,1840,596],{"className":1841,"style":664},[659,663],[572,1843,1845],{"className":1844},[668],[572,1846,1848,1868],{"className":1847},[672,989],[572,1849,1851,1865],{"className":1850},[676],[572,1852,1854],{"className":1853,"style":1171},[680],[572,1855,1856,1859],{"style":999},[572,1857],{"className":1858,"style":689},[688],[572,1860,1862],{"className":1861},[693,694,695,696],[572,1863,564],{"className":1864},[659,663,696],[572,1866,1013],{"className":1867},[1012],[572,1869,1871],{"className":1870},[676],[572,1872,1874],{"className":1873,"style":1192},[680],[572,1875],{},". Das Ergebnis ist dasselbe wie mit der Lösungsformel für lineare DGL erster Ordnung; die Variation der Konstanten zeigt, woher diese Formel kommt.",[564,1878,1879,1880,1090],{},"Das Verfahren funktioniert für jede stetige Störfunktion, auch wenn ein Ansatz vom Typ der rechten Seite versagt. Es lässt sich auf lineare Gleichungen höherer Ordnung übertragen; dort variiert man alle Konstanten der homogenen Lösung und erhält ein lineares Gleichungssystem für die ",[572,1881,1883,1911],{"className":1882},[575],[572,1884,1886],{"className":1885},[579],[581,1887,1888],{"xmlns":583},[585,1889,1890,1908],{},[588,1891,1892,1902,1904,1906],{},[1893,1894,1895,1897,1900],"msubsup",{},[594,1896,942],{},[594,1898,1899],{},"i",[598,1901,602],{"mathvariant":600,"lspace":601,"rspace":601},[598,1903,612],{"stretchy":611},[594,1905,615],{},[598,1907,618],{"stretchy":611},[638,1909,1910],{"encoding":640},"C_i'(x)",[572,1912,1914],{"className":1913,"ariaHidden":646},[645],[572,1915,1917,1921,1977,1980,1983],{"className":1916},[650],[572,1918],{"className":1919,"style":1920},[654],"height:1.0106em;vertical-align:-0.2587em;",[572,1922,1924,1927],{"className":1923},[659],[572,1925,942],{"className":1926,"style":1042},[659,663],[572,1928,1930],{"className":1929},[668],[572,1931,1933,1968],{"className":1932},[672,989],[572,1934,1936,1965],{"className":1935},[676],[572,1937,1939,1951],{"className":1938,"style":681},[680],[572,1940,1942,1945],{"style":1941},"top:-2.4413em;margin-left:-0.0715em;margin-right:0.05em;",[572,1943],{"className":1944,"style":689},[688],[572,1946,1948],{"className":1947},[693,694,695,696],[572,1949,1899],{"className":1950},[659,663,696],[572,1952,1953,1956],{"style":684},[572,1954],{"className":1955,"style":689},[688],[572,1957,1959],{"className":1958},[693,694,695,696],[572,1960,1962],{"className":1961},[659,696],[572,1963,602],{"className":1964},[659,696],[572,1966,1013],{"className":1967},[1012],[572,1969,1971],{"className":1970},[676],[572,1972,1975],{"className":1973,"style":1974},[680],"height:0.2587em;",[572,1976],{},[572,1978,612],{"className":1979},[728],[572,1981,615],{"className":1982},[659,663],[572,1984,618],{"className":1985},[735],[559,1987,1989],{"id":1988},"beispiele","Beispiele",[564,1991,1992,2099,2100,2158,2159,2231,2232,2369,2370,2520],{},[572,1993,1995,2021],{"className":1994},[575],[572,1996,1998],{"className":1997},[579],[581,1999,2000],{"xmlns":583},[585,2001,2002,2018],{},[588,2003,2004,2010,2012,2014,2016],{},[591,2005,2006,2008],{},[594,2007,596],{},[598,2009,602],{"mathvariant":600,"lspace":601,"rspace":601},[598,2011,954],{},[594,2013,596],{},[598,2015,627],{},[594,2017,615],{},[638,2019,2020],{"encoding":640},"y' - y = x",[572,2022,2024,2071,2089],{"className":2023,"ariaHidden":646},[645],[572,2025,2027,2030,2062,2065,2068],{"className":2026},[650],[572,2028],{"className":2029,"style":655},[654],[572,2031,2033,2036],{"className":2032},[659],[572,2034,596],{"className":2035,"style":664},[659,663],[572,2037,2039],{"className":2038},[668],[572,2040,2042],{"className":2041},[672],[572,2043,2045],{"className":2044},[676],[572,2046,2048],{"className":2047,"style":681},[680],[572,2049,2050,2053],{"style":684},[572,2051],{"className":2052,"style":689},[688],[572,2054,2056],{"className":2055},[693,694,695,696],[572,2057,2059],{"className":2058},[659,696],[572,2060,602],{"className":2061},[659,696],[572,2063],{"className":2064,"style":707},[706],[572,2066,954],{"className":2067},[711],[572,2069],{"className":2070,"style":707},[706],[572,2072,2074,2077,2080,2083,2086],{"className":2073},[650],[572,2075],{"className":2076,"style":976},[654],[572,2078,596],{"className":2079,"style":664},[659,663],[572,2081],{"className":2082,"style":746},[706],[572,2084,627],{"className":2085},[750],[572,2087],{"className":2088,"style":746},[706],[572,2090,2092,2096],{"className":2091},[650],[572,2093],{"className":2094,"style":2095},[654],"height:0.4306em;",[572,2097,615],{"className":2098},[659,663],". Hier ist ",[572,2101,2103,2124],{"className":2102},[575],[572,2104,2106],{"className":2105},[579],[581,2107,2108],{"xmlns":583},[585,2109,2110,2121],{},[588,2111,2112,2114,2116,2118],{},[594,2113,608],{},[598,2115,627],{},[598,2117,954],{},[818,2119,2120],{},"1",[638,2122,2123],{"encoding":640},"a = -1",[572,2125,2127,2145],{"className":2126,"ariaHidden":646},[645],[572,2128,2130,2133,2136,2139,2142],{"className":2129},[650],[572,2131],{"className":2132,"style":2095},[654],[572,2134,608],{"className":2135},[659,663],[572,2137],{"className":2138,"style":746},[706],[572,2140,627],{"className":2141},[750],[572,2143],{"className":2144,"style":746},[706],[572,2146,2148,2152,2155],{"className":2147},[650],[572,2149],{"className":2150,"style":2151},[654],"height:0.7278em;vertical-align:-0.0833em;",[572,2153,954],{"className":2154},[659],[572,2156,2120],{"className":2157},[659],", ",[572,2160,2162,2188],{"className":2161},[575],[572,2163,2165],{"className":2164},[579],[581,2166,2167],{"xmlns":583},[585,2168,2169,2185],{},[588,2170,2171,2173,2175,2177,2179,2181,2183],{},[594,2172,957],{},[598,2174,612],{"stretchy":611},[594,2176,615],{},[598,2178,618],{"stretchy":611},[598,2180,627],{},[598,2182,954],{},[594,2184,615],{},[638,2186,2187],{"encoding":640},"A(x) = -x",[572,2189,2191,2218],{"className":2190,"ariaHidden":646},[645],[572,2192,2194,2197,2200,2203,2206,2209,2212,2215],{"className":2193},[650],[572,2195],{"className":2196,"style":721},[654],[572,2198,957],{"className":2199},[659,663],[572,2201,612],{"className":2202},[728],[572,2204,615],{"className":2205},[659,663],[572,2207,618],{"className":2208},[735],[572,2210],{"className":2211,"style":746},[706],[572,2213,627],{"className":2214},[750],[572,2216],{"className":2217,"style":746},[706],[572,2219,2221,2225,2228],{"className":2220},[650],[572,2222],{"className":2223,"style":2224},[654],"height:0.6667em;vertical-align:-0.0833em;",[572,2226,954],{"className":2227},[659],[572,2229,615],{"className":2230},[659,663],", die homogene Lösung ",[572,2233,2235,2265],{"className":2234},[575],[572,2236,2238],{"className":2237},[579],[581,2239,2240],{"xmlns":583},[585,2241,2242,2262],{},[588,2243,2244,2250,2252,2254,2256],{},[931,2245,2246,2248],{},[594,2247,596],{},[594,2249,937],{},[598,2251,627],{},[594,2253,942],{},[620,2255,622],{},[591,2257,2258,2260],{},[594,2259,949],{},[594,2261,615],{},[638,2263,2264],{"encoding":640},"y_h = C\\,e^{x}",[572,2266,2268,2323],{"className":2267,"ariaHidden":646},[645],[572,2269,2271,2274,2314,2317,2320],{"className":2270},[650],[572,2272],{"className":2273,"style":976},[654],[572,2275,2277,2280],{"className":2276},[659],[572,2278,596],{"className":2279,"style":664},[659,663],[572,2281,2283],{"className":2282},[668],[572,2284,2286,2306],{"className":2285},[672,989],[572,2287,2289,2303],{"className":2288},[676],[572,2290,2292],{"className":2291,"style":996},[680],[572,2293,2294,2297],{"style":999},[572,2295],{"className":2296,"style":689},[688],[572,2298,2300],{"className":2299},[693,694,695,696],[572,2301,937],{"className":2302},[659,663,696],[572,2304,1013],{"className":2305},[1012],[572,2307,2309],{"className":2308},[676],[572,2310,2312],{"className":2311,"style":1020},[680],[572,2313],{},[572,2315],{"className":2316,"style":746},[706],[572,2318,627],{"className":2319},[750],[572,2321],{"className":2322,"style":746},[706],[572,2324,2326,2330,2333,2336],{"className":2325},[650],[572,2327],{"className":2328,"style":2329},[654],"height:0.6833em;",[572,2331,942],{"className":2332,"style":1042},[659,663],[572,2334],{"className":2335,"style":739},[706],[572,2337,2339,2342],{"className":2338},[659],[572,2340,949],{"className":2341},[659,663],[572,2343,2345],{"className":2344},[668],[572,2346,2348],{"className":2347},[672],[572,2349,2351],{"className":2350},[676],[572,2352,2355],{"className":2353,"style":2354},[680],"height:0.6644em;",[572,2356,2357,2360],{"style":684},[572,2358],{"className":2359,"style":689},[688],[572,2361,2363],{"className":2362},[693,694,695,696],[572,2364,2366],{"className":2365},[659,696],[572,2367,615],{"className":2368},[659,663,696],". Ansatz ",[572,2371,2373,2409],{"className":2372},[575],[572,2374,2376],{"className":2375},[579],[581,2377,2378],{"xmlns":583},[585,2379,2380,2406],{},[588,2381,2382,2388,2390,2392,2394,2396,2398,2400],{},[931,2383,2384,2386],{},[594,2385,596],{},[594,2387,564],{},[598,2389,627],{},[594,2391,942],{},[598,2393,612],{"stretchy":611},[594,2395,615],{},[598,2397,618],{"stretchy":611},[620,2399,622],{},[591,2401,2402,2404],{},[594,2403,949],{},[594,2405,615],{},[638,2407,2408],{"encoding":640},"y_p = C(x)\\,e^{x}",[572,2410,2412,2467],{"className":2411,"ariaHidden":646},[645],[572,2413,2415,2418,2458,2461,2464],{"className":2414},[650],[572,2416],{"className":2417,"style":1152},[654],[572,2419,2421,2424],{"className":2420},[659],[572,2422,596],{"className":2423,"style":664},[659,663],[572,2425,2427],{"className":2426},[668],[572,2428,2430,2450],{"className":2429},[672,989],[572,2431,2433,2447],{"className":2432},[676],[572,2434,2436],{"className":2435,"style":1171},[680],[572,2437,2438,2441],{"style":999},[572,2439],{"className":2440,"style":689},[688],[572,2442,2444],{"className":2443},[693,694,695,696],[572,2445,564],{"className":2446},[659,663,696],[572,2448,1013],{"className":2449},[1012],[572,2451,2453],{"className":2452},[676],[572,2454,2456],{"className":2455,"style":1192},[680],[572,2457],{},[572,2459],{"className":2460,"style":746},[706],[572,2462,627],{"className":2463},[750],[572,2465],{"className":2466,"style":746},[706],[572,2468,2470,2473,2476,2479,2482,2485,2488],{"className":2469},[650],[572,2471],{"className":2472,"style":721},[654],[572,2474,942],{"className":2475,"style":1042},[659,663],[572,2477,612],{"className":2478},[728],[572,2480,615],{"className":2481},[659,663],[572,2483,618],{"className":2484},[735],[572,2486],{"className":2487,"style":739},[706],[572,2489,2491,2494],{"className":2490},[659],[572,2492,949],{"className":2493},[659,663],[572,2495,2497],{"className":2496},[668],[572,2498,2500],{"className":2499},[672],[572,2501,2503],{"className":2502},[676],[572,2504,2506],{"className":2505,"style":2354},[680],[572,2507,2508,2511],{"style":684},[572,2509],{"className":2510,"style":689},[688],[572,2512,2514],{"className":2513},[693,694,695,696],[572,2515,2517],{"className":2516},[659,696],[572,2518,615],{"className":2519},[659,663,696],":",[572,2522,2525],{"className":2523},[2524],"katex-display",[572,2526,2528,2641],{"className":2527},[575],[572,2529,2531],{"className":2530},[579],[581,2532,2534],{"xmlns":583,"display":2533},"block",[585,2535,2536,2638],{},[588,2537,2538,2544,2546,2548,2550,2552,2558,2560,2562,2565,2568,2570,2576,2578,2580,2582,2584,2586,2588,2598,2600,2602,2604,2606,2608,2610,2612,2614,2616,2618,2620,2622,2624,2626,2628],{},[591,2539,2540,2542],{},[594,2541,942],{},[598,2543,602],{"mathvariant":600,"lspace":601,"rspace":601},[598,2545,612],{"stretchy":611},[594,2547,615],{},[598,2549,618],{"stretchy":611},[620,2551,622],{},[591,2553,2554,2556],{},[594,2555,949],{},[594,2557,615],{},[598,2559,627],{},[594,2561,615],{},[706,2563],{"width":2564},"1em",[598,2566,2567],{},"⇒",[706,2569],{"width":2564},[591,2571,2572,2574],{},[594,2573,942],{},[598,2575,602],{"mathvariant":600,"lspace":601,"rspace":601},[598,2577,612],{"stretchy":611},[594,2579,615],{},[598,2581,618],{"stretchy":611},[598,2583,627],{},[594,2585,615],{},[620,2587,622],{},[591,2589,2590,2592],{},[594,2591,949],{},[588,2593,2594,2596],{},[598,2595,954],{},[594,2597,615],{},[706,2599],{"width":2564},[598,2601,2567],{},[706,2603],{"width":2564},[594,2605,942],{},[598,2607,612],{"stretchy":611},[594,2609,615],{},[598,2611,618],{"stretchy":611},[598,2613,627],{},[598,2615,954],{},[598,2617,612],{"stretchy":611},[594,2619,615],{},[598,2621,605],{},[818,2623,2120],{},[598,2625,618],{"stretchy":611},[620,2627,622],{},[591,2629,2630,2632],{},[594,2631,949],{},[588,2633,2634,2636],{},[598,2635,954],{},[594,2637,615],{},[638,2639,2640],{"encoding":640},"C'(x)\\,e^{x} = x \\quad\\Rightarrow\\quad C'(x) = x\\,e^{-x} \\quad\\Rightarrow\\quad C(x) = -(x + 1)\\,e^{-x}",[572,2642,2644,2739,2764,2820,2883,2910,2934],{"className":2643,"ariaHidden":646},[645],[572,2645,2647,2651,2685,2688,2691,2694,2697,2730,2733,2736],{"className":2646},[650],[572,2648],{"className":2649,"style":2650},[654],"height:1.0519em;vertical-align:-0.25em;",[572,2652,2654,2657],{"className":2653},[659],[572,2655,942],{"className":2656,"style":1042},[659,663],[572,2658,2660],{"className":2659},[668],[572,2661,2663],{"className":2662},[672],[572,2664,2666],{"className":2665},[676],[572,2667,2670],{"className":2668,"style":2669},[680],"height:0.8019em;",[572,2671,2673,2676],{"style":2672},"top:-3.113em;margin-right:0.05em;",[572,2674],{"className":2675,"style":689},[688],[572,2677,2679],{"className":2678},[693,694,695,696],[572,2680,2682],{"className":2681},[659,696],[572,2683,602],{"className":2684},[659,696],[572,2686,612],{"className":2687},[728],[572,2689,615],{"className":2690},[659,663],[572,2692,618],{"className":2693},[735],[572,2695],{"className":2696,"style":739},[706],[572,2698,2700,2703],{"className":2699},[659],[572,2701,949],{"className":2702},[659,663],[572,2704,2706],{"className":2705},[668],[572,2707,2709],{"className":2708},[672],[572,2710,2712],{"className":2711},[676],[572,2713,2716],{"className":2714,"style":2715},[680],"height:0.7144em;",[572,2717,2718,2721],{"style":2672},[572,2719],{"className":2720,"style":689},[688],[572,2722,2724],{"className":2723},[693,694,695,696],[572,2725,2727],{"className":2726},[659,696],[572,2728,615],{"className":2729},[659,663,696],[572,2731],{"className":2732,"style":746},[706],[572,2734,627],{"className":2735},[750],[572,2737],{"className":2738,"style":746},[706],[572,2740,2742,2745,2748,2752,2755,2758,2761],{"className":2741},[650],[572,2743],{"className":2744,"style":2095},[654],[572,2746,615],{"className":2747},[659,663],[572,2749],{"className":2750,"style":2751},[706],"margin-right:1em;",[572,2753],{"className":2754,"style":746},[706],[572,2756,2567],{"className":2757},[750],[572,2759],{"className":2760,"style":2751},[706],[572,2762],{"className":2763,"style":746},[706],[572,2765,2767,2770,2802,2805,2808,2811,2814,2817],{"className":2766},[650],[572,2768],{"className":2769,"style":2650},[654],[572,2771,2773,2776],{"className":2772},[659],[572,2774,942],{"className":2775,"style":1042},[659,663],[572,2777,2779],{"className":2778},[668],[572,2780,2782],{"className":2781},[672],[572,2783,2785],{"className":2784},[676],[572,2786,2788],{"className":2787,"style":2669},[680],[572,2789,2790,2793],{"style":2672},[572,2791],{"className":2792,"style":689},[688],[572,2794,2796],{"className":2795},[693,694,695,696],[572,2797,2799],{"className":2798},[659,696],[572,2800,602],{"className":2801},[659,696],[572,2803,612],{"className":2804},[728],[572,2806,615],{"className":2807},[659,663],[572,2809,618],{"className":2810},[735],[572,2812],{"className":2813,"style":746},[706],[572,2815,627],{"className":2816},[750],[572,2818],{"className":2819,"style":746},[706],[572,2821,2823,2827,2830,2833,2868,2871,2874,2877,2880],{"className":2822},[650],[572,2824],{"className":2825,"style":2826},[654],"height:0.8213em;",[572,2828,615],{"className":2829},[659,663],[572,2831],{"className":2832,"style":739},[706],[572,2834,2836,2839],{"className":2835},[659],[572,2837,949],{"className":2838},[659,663],[572,2840,2842],{"className":2841},[668],[572,2843,2845],{"className":2844},[672],[572,2846,2848],{"className":2847},[676],[572,2849,2851],{"className":2850,"style":2826},[680],[572,2852,2853,2856],{"style":2672},[572,2854],{"className":2855,"style":689},[688],[572,2857,2859],{"className":2858},[693,694,695,696],[572,2860,2862,2865],{"className":2861},[659,696],[572,2863,954],{"className":2864},[659,696],[572,2866,615],{"className":2867},[659,663,696],[572,2869],{"className":2870,"style":2751},[706],[572,2872],{"className":2873,"style":746},[706],[572,2875,2567],{"className":2876},[750],[572,2878],{"className":2879,"style":2751},[706],[572,2881],{"className":2882,"style":746},[706],[572,2884,2886,2889,2892,2895,2898,2901,2904,2907],{"className":2885},[650],[572,2887],{"className":2888,"style":721},[654],[572,2890,942],{"className":2891,"style":1042},[659,663],[572,2893,612],{"className":2894},[728],[572,2896,615],{"className":2897},[659,663],[572,2899,618],{"className":2900},[735],[572,2902],{"className":2903,"style":746},[706],[572,2905,627],{"className":2906},[750],[572,2908],{"className":2909,"style":746},[706],[572,2911,2913,2916,2919,2922,2925,2928,2931],{"className":2912},[650],[572,2914],{"className":2915,"style":721},[654],[572,2917,954],{"className":2918},[659],[572,2920,612],{"className":2921},[728],[572,2923,615],{"className":2924},[659,663],[572,2926],{"className":2927,"style":707},[706],[572,2929,605],{"className":2930},[711],[572,2932],{"className":2933,"style":707},[706],[572,2935,2937,2941,2944,2947,2950],{"className":2936},[650],[572,2938],{"className":2939,"style":2940},[654],"height:1.0713em;vertical-align:-0.25em;",[572,2942,2120],{"className":2943},[659],[572,2945,618],{"className":2946},[735],[572,2948],{"className":2949,"style":739},[706],[572,2951,2953,2956],{"className":2952},[659],[572,2954,949],{"className":2955},[659,663],[572,2957,2959],{"className":2958},[668],[572,2960,2962],{"className":2961},[672],[572,2963,2965],{"className":2964},[676],[572,2966,2968],{"className":2967,"style":2826},[680],[572,2969,2970,2973],{"style":2672},[572,2971],{"className":2972,"style":689},[688],[572,2974,2976],{"className":2975},[693,694,695,696],[572,2977,2979,2982],{"className":2978},[659,696],[572,2980,954],{"className":2981},[659,696],[572,2983,615],{"className":2984},[659,663,696],[564,2986,2987,2988,3117],{},"(partielle Integration; Probe durch Ableiten). Damit ist ",[572,2989,2991,3023],{"className":2990},[575],[572,2992,2994],{"className":2993},[579],[581,2995,2996],{"xmlns":583},[585,2997,2998,3020],{},[588,2999,3000,3006,3008,3010,3012,3014,3016,3018],{},[931,3001,3002,3004],{},[594,3003,596],{},[594,3005,564],{},[598,3007,627],{},[598,3009,954],{},[598,3011,612],{"stretchy":611},[594,3013,615],{},[598,3015,605],{},[818,3017,2120],{},[598,3019,618],{"stretchy":611},[638,3021,3022],{"encoding":640},"y_p = -(x + 1)",[572,3024,3026,3081,3105],{"className":3025,"ariaHidden":646},[645],[572,3027,3029,3032,3072,3075,3078],{"className":3028},[650],[572,3030],{"className":3031,"style":1152},[654],[572,3033,3035,3038],{"className":3034},[659],[572,3036,596],{"className":3037,"style":664},[659,663],[572,3039,3041],{"className":3040},[668],[572,3042,3044,3064],{"className":3043},[672,989],[572,3045,3047,3061],{"className":3046},[676],[572,3048,3050],{"className":3049,"style":1171},[680],[572,3051,3052,3055],{"style":999},[572,3053],{"className":3054,"style":689},[688],[572,3056,3058],{"className":3057},[693,694,695,696],[572,3059,564],{"className":3060},[659,663,696],[572,3062,1013],{"className":3063},[1012],[572,3065,3067],{"className":3066},[676],[572,3068,3070],{"className":3069,"style":1192},[680],[572,3071],{},[572,3073],{"className":3074,"style":746},[706],[572,3076,627],{"className":3077},[750],[572,3079],{"className":3080,"style":746},[706],[572,3082,3084,3087,3090,3093,3096,3099,3102],{"className":3083},[650],[572,3085],{"className":3086,"style":721},[654],[572,3088,954],{"className":3089},[659],[572,3091,612],{"className":3092},[728],[572,3094,615],{"className":3095},[659,663],[572,3097],{"className":3098,"style":707},[706],[572,3100,605],{"className":3101},[711],[572,3103],{"className":3104,"style":707},[706],[572,3106,3108,3111,3114],{"className":3107},[650],[572,3109],{"className":3110,"style":721},[654],[572,3112,2120],{"className":3113},[659],[572,3115,618],{"className":3116},[735]," und die allgemeine Lösung",[572,3119,3121],{"className":3120},[2524],[572,3122,3124,3159],{"className":3123},[575],[572,3125,3127],{"className":3126},[579],[581,3128,3129],{"xmlns":583,"display":2533},[585,3130,3131,3156],{},[588,3132,3133,3135,3137,3140,3142,3148,3150,3152,3154],{},[594,3134,596],{},[598,3136,627],{},[594,3138,3139],{},"K",[620,3141,622],{},[591,3143,3144,3146],{},[594,3145,949],{},[594,3147,615],{},[598,3149,954],{},[594,3151,615],{},[598,3153,954],{},[818,3155,2120],{},[638,3157,3158],{"encoding":640},"y = K\\,e^{x} - x - 1",[572,3160,3162,3180,3234,3252],{"className":3161,"ariaHidden":646},[645],[572,3163,3165,3168,3171,3174,3177],{"className":3164},[650],[572,3166],{"className":3167,"style":976},[654],[572,3169,596],{"className":3170,"style":664},[659,663],[572,3172],{"className":3173,"style":746},[706],[572,3175,627],{"className":3176},[750],[572,3178],{"className":3179,"style":746},[706],[572,3181,3183,3187,3190,3193,3225,3228,3231],{"className":3182},[650],[572,3184],{"className":3185,"style":3186},[654],"height:0.7977em;vertical-align:-0.0833em;",[572,3188,3139],{"className":3189,"style":1042},[659,663],[572,3191],{"className":3192,"style":739},[706],[572,3194,3196,3199],{"className":3195},[659],[572,3197,949],{"className":3198},[659,663],[572,3200,3202],{"className":3201},[668],[572,3203,3205],{"className":3204},[672],[572,3206,3208],{"className":3207},[676],[572,3209,3211],{"className":3210,"style":2715},[680],[572,3212,3213,3216],{"style":2672},[572,3214],{"className":3215,"style":689},[688],[572,3217,3219],{"className":3218},[693,694,695,696],[572,3220,3222],{"className":3221},[659,696],[572,3223,615],{"className":3224},[659,663,696],[572,3226],{"className":3227,"style":707},[706],[572,3229,954],{"className":3230},[711],[572,3232],{"className":3233,"style":707},[706],[572,3235,3237,3240,3243,3246,3249],{"className":3236},[650],[572,3238],{"className":3239,"style":2224},[654],[572,3241,615],{"className":3242},[659,663],[572,3244],{"className":3245,"style":707},[706],[572,3247,954],{"className":3248},[711],[572,3250],{"className":3251,"style":707},[706],[572,3253,3255,3258],{"className":3254},[650],[572,3256],{"className":3257,"style":913},[654],[572,3259,2120],{"className":3260},[659],[564,3262,3263,3264,1090],{},"Probe: ",[572,3265,3267,3313],{"className":3266},[575],[572,3268,3270],{"className":3269},[579],[581,3271,3272],{"xmlns":583},[585,3273,3274,3310],{},[588,3275,3276,3284,3286,3292,3294,3296,3298,3300,3302,3304,3306,3308],{},[1893,3277,3278,3280,3282],{},[594,3279,596],{},[594,3281,564],{},[598,3283,602],{"mathvariant":600,"lspace":601,"rspace":601},[598,3285,954],{},[931,3287,3288,3290],{},[594,3289,596],{},[594,3291,564],{},[598,3293,627],{},[598,3295,954],{},[818,3297,2120],{},[598,3299,605],{},[594,3301,615],{},[598,3303,605],{},[818,3305,2120],{},[598,3307,627],{},[594,3309,615],{},[638,3311,3312],{"encoding":640},"y_p' - y_p = -1 + x + 1 = x",[572,3314,3316,3388,3443,3464,3482,3500],{"className":3315,"ariaHidden":646},[645],[572,3317,3319,3323,3379,3382,3385],{"className":3318},[650],[572,3320],{"className":3321,"style":3322},[654],"height:1.135em;vertical-align:-0.3831em;",[572,3324,3326,3329],{"className":3325},[659],[572,3327,596],{"className":3328,"style":664},[659,663],[572,3330,3332],{"className":3331},[668],[572,3333,3335,3370],{"className":3334},[672,989],[572,3336,3338,3367],{"className":3337},[676],[572,3339,3341,3353],{"className":3340,"style":681},[680],[572,3342,3344,3347],{"style":3343},"top:-2.453em;margin-left:-0.0359em;margin-right:0.05em;",[572,3345],{"className":3346,"style":689},[688],[572,3348,3350],{"className":3349},[693,694,695,696],[572,3351,564],{"className":3352},[659,663,696],[572,3354,3355,3358],{"style":684},[572,3356],{"className":3357,"style":689},[688],[572,3359,3361],{"className":3360},[693,694,695,696],[572,3362,3364],{"className":3363},[659,696],[572,3365,602],{"className":3366},[659,696],[572,3368,1013],{"className":3369},[1012],[572,3371,3373],{"className":3372},[676],[572,3374,3377],{"className":3375,"style":3376},[680],"height:0.3831em;",[572,3378],{},[572,3380],{"className":3381,"style":707},[706],[572,3383,954],{"className":3384},[711],[572,3386],{"className":3387,"style":707},[706],[572,3389,3391,3394,3434,3437,3440],{"className":3390},[650],[572,3392],{"className":3393,"style":1152},[654],[572,3395,3397,3400],{"className":3396},[659],[572,3398,596],{"className":3399,"style":664},[659,663],[572,3401,3403],{"className":3402},[668],[572,3404,3406,3426],{"className":3405},[672,989],[572,3407,3409,3423],{"className":3408},[676],[572,3410,3412],{"className":3411,"style":1171},[680],[572,3413,3414,3417],{"style":999},[572,3415],{"className":3416,"style":689},[688],[572,3418,3420],{"className":3419},[693,694,695,696],[572,3421,564],{"className":3422},[659,663,696],[572,3424,1013],{"className":3425},[1012],[572,3427,3429],{"className":3428},[676],[572,3430,3432],{"className":3431,"style":1192},[680],[572,3433],{},[572,3435],{"className":3436,"style":746},[706],[572,3438,627],{"className":3439},[750],[572,3441],{"className":3442,"style":746},[706],[572,3444,3446,3449,3452,3455,3458,3461],{"className":3445},[650],[572,3447],{"className":3448,"style":2151},[654],[572,3450,954],{"className":3451},[659],[572,3453,2120],{"className":3454},[659],[572,3456],{"className":3457,"style":707},[706],[572,3459,605],{"className":3460},[711],[572,3462],{"className":3463,"style":707},[706],[572,3465,3467,3470,3473,3476,3479],{"className":3466},[650],[572,3468],{"className":3469,"style":2224},[654],[572,3471,615],{"className":3472},[659,663],[572,3474],{"className":3475,"style":707},[706],[572,3477,605],{"className":3478},[711],[572,3480],{"className":3481,"style":707},[706],[572,3483,3485,3488,3491,3494,3497],{"className":3484},[650],[572,3486],{"className":3487,"style":913},[654],[572,3489,2120],{"className":3490},[659],[572,3492],{"className":3493,"style":746},[706],[572,3495,627],{"className":3496},[750],[572,3498],{"className":3499,"style":746},[706],[572,3501,3503,3506],{"className":3502},[650],[572,3504],{"className":3505,"style":2095},[654],[572,3507,615],{"className":3508},[659,663],[564,3510,3511,3670,3671,3755,3756,3904],{},[572,3512,3514,3553],{"className":3513},[575],[572,3515,3517],{"className":3516},[579],[581,3518,3519],{"xmlns":583},[585,3520,3521,3550],{},[588,3522,3523,3529,3531,3534,3536,3538],{},[591,3524,3525,3527],{},[594,3526,596],{},[598,3528,602],{"mathvariant":600,"lspace":601,"rspace":601},[598,3530,605],{},[818,3532,3533],{},"2",[594,3535,596],{},[598,3537,627],{},[591,3539,3540,3542],{},[594,3541,949],{},[588,3543,3544,3546,3548],{},[598,3545,954],{},[818,3547,3533],{},[594,3549,615],{},[638,3551,3552],{"encoding":640},"y' + 2y = e^{-2x}",[572,3554,3556,3603,3625],{"className":3555,"ariaHidden":646},[645],[572,3557,3559,3562,3594,3597,3600],{"className":3558},[650],[572,3560],{"className":3561,"style":655},[654],[572,3563,3565,3568],{"className":3564},[659],[572,3566,596],{"className":3567,"style":664},[659,663],[572,3569,3571],{"className":3570},[668],[572,3572,3574],{"className":3573},[672],[572,3575,3577],{"className":3576},[676],[572,3578,3580],{"className":3579,"style":681},[680],[572,3581,3582,3585],{"style":684},[572,3583],{"className":3584,"style":689},[688],[572,3586,3588],{"className":3587},[693,694,695,696],[572,3589,3591],{"className":3590},[659,696],[572,3592,602],{"className":3593},[659,696],[572,3595],{"className":3596,"style":707},[706],[572,3598,605],{"className":3599},[711],[572,3601],{"className":3602,"style":707},[706],[572,3604,3606,3610,3613,3616,3619,3622],{"className":3605},[650],[572,3607],{"className":3608,"style":3609},[654],"height:0.8389em;vertical-align:-0.1944em;",[572,3611,3533],{"className":3612},[659],[572,3614,596],{"className":3615,"style":664},[659,663],[572,3617],{"className":3618,"style":746},[706],[572,3620,627],{"className":3621},[750],[572,3623],{"className":3624,"style":746},[706],[572,3626,3628,3632],{"className":3627},[650],[572,3629],{"className":3630,"style":3631},[654],"height:0.8141em;",[572,3633,3635,3638],{"className":3634},[659],[572,3636,949],{"className":3637},[659,663],[572,3639,3641],{"className":3640},[668],[572,3642,3644],{"className":3643},[672],[572,3645,3647],{"className":3646},[676],[572,3648,3650],{"className":3649,"style":3631},[680],[572,3651,3652,3655],{"style":684},[572,3653],{"className":3654,"style":689},[688],[572,3656,3658],{"className":3657},[693,694,695,696],[572,3659,3661,3664,3667],{"className":3660},[659,696],[572,3662,954],{"className":3663},[659,696],[572,3665,3533],{"className":3666},[659,696],[572,3668,615],{"className":3669},[659,663,696],". Die homogene Lösung ist ",[572,3672,3674,3702],{"className":3673},[575],[572,3675,3677],{"className":3676},[579],[581,3678,3679],{"xmlns":583},[585,3680,3681,3699],{},[588,3682,3683,3685,3687],{},[594,3684,942],{},[620,3686,622],{},[591,3688,3689,3691],{},[594,3690,949],{},[588,3692,3693,3695,3697],{},[598,3694,954],{},[818,3696,3533],{},[594,3698,615],{},[638,3700,3701],{"encoding":640},"C\\,e^{-2x}",[572,3703,3705],{"className":3704,"ariaHidden":646},[645],[572,3706,3708,3711,3714,3717],{"className":3707},[650],[572,3709],{"className":3710,"style":3631},[654],[572,3712,942],{"className":3713,"style":1042},[659,663],[572,3715],{"className":3716,"style":739},[706],[572,3718,3720,3723],{"className":3719},[659],[572,3721,949],{"className":3722},[659,663],[572,3724,3726],{"className":3725},[668],[572,3727,3729],{"className":3728},[672],[572,3730,3732],{"className":3731},[676],[572,3733,3735],{"className":3734,"style":3631},[680],[572,3736,3737,3740],{"style":684},[572,3738],{"className":3739,"style":689},[688],[572,3741,3743],{"className":3742},[693,694,695,696],[572,3744,3746,3749,3752],{"className":3745},[659,696],[572,3747,954],{"className":3748},[659,696],[572,3750,3533],{"className":3751},[659,696],[572,3753,615],{"className":3754},[659,663,696],". Ein Ansatz ",[572,3757,3759,3796],{"className":3758},[575],[572,3760,3762],{"className":3761},[579],[581,3763,3764],{"xmlns":583},[585,3765,3766,3793],{},[588,3767,3768,3774,3776,3779,3781],{},[931,3769,3770,3772],{},[594,3771,596],{},[594,3773,564],{},[598,3775,627],{},[594,3777,3778],{},"c",[620,3780,622],{},[591,3782,3783,3785],{},[594,3784,949],{},[588,3786,3787,3789,3791],{},[598,3788,954],{},[818,3790,3533],{},[594,3792,615],{},[638,3794,3795],{"encoding":640},"y_p = c\\,e^{-2x}",[572,3797,3799,3854],{"className":3798,"ariaHidden":646},[645],[572,3800,3802,3805,3845,3848,3851],{"className":3801},[650],[572,3803],{"className":3804,"style":1152},[654],[572,3806,3808,3811],{"className":3807},[659],[572,3809,596],{"className":3810,"style":664},[659,663],[572,3812,3814],{"className":3813},[668],[572,3815,3817,3837],{"className":3816},[672,989],[572,3818,3820,3834],{"className":3819},[676],[572,3821,3823],{"className":3822,"style":1171},[680],[572,3824,3825,3828],{"style":999},[572,3826],{"className":3827,"style":689},[688],[572,3829,3831],{"className":3830},[693,694,695,696],[572,3832,564],{"className":3833},[659,663,696],[572,3835,1013],{"className":3836},[1012],[572,3838,3840],{"className":3839},[676],[572,3841,3843],{"className":3842,"style":1192},[680],[572,3844],{},[572,3846],{"className":3847,"style":746},[706],[572,3849,627],{"className":3850},[750],[572,3852],{"className":3853,"style":746},[706],[572,3855,3857,3860,3863,3866],{"className":3856},[650],[572,3858],{"className":3859,"style":3631},[654],[572,3861,3778],{"className":3862},[659,663],[572,3864],{"className":3865,"style":739},[706],[572,3867,3869,3872],{"className":3868},[659],[572,3870,949],{"className":3871},[659,663],[572,3873,3875],{"className":3874},[668],[572,3876,3878],{"className":3877},[672],[572,3879,3881],{"className":3880},[676],[572,3882,3884],{"className":3883,"style":3631},[680],[572,3885,3886,3889],{"style":684},[572,3887],{"className":3888,"style":689},[688],[572,3890,3892],{"className":3891},[693,694,695,696],[572,3893,3895,3898,3901],{"className":3894},[659,696],[572,3896,954],{"className":3897},[659,696],[572,3899,3533],{"className":3900},[659,696],[572,3902,615],{"className":3903},[659,663,696]," scheitert, weil er selbst homogene Lösung ist. Mit der Variation der Konstanten:",[572,3906,3908],{"className":3907},[2524],[572,3909,3911,4014],{"className":3910},[575],[572,3912,3914],{"className":3913},[579],[581,3915,3916],{"xmlns":583,"display":2533},[585,3917,3918,4011],{},[588,3919,3920,3926,3928,3930,3932,3934,3946,3949,3959,3961,3963,3965,3967,3969,3971,3973,3975,3977,3979,3981,3983,3985,3987,3993,3995,3997,3999],{},[591,3921,3922,3924],{},[594,3923,942],{},[598,3925,602],{"mathvariant":600,"lspace":601,"rspace":601},[598,3927,612],{"stretchy":611},[594,3929,615],{},[598,3931,618],{"stretchy":611},[598,3933,627],{},[591,3935,3936,3938],{},[594,3937,949],{},[588,3939,3940,3942,3944],{},[598,3941,954],{},[818,3943,3533],{},[594,3945,615],{},[598,3947,3948],{},"⋅",[591,3950,3951,3953],{},[594,3952,949],{},[588,3954,3955,3957],{},[818,3956,3533],{},[594,3958,615],{},[598,3960,627],{},[818,3962,2120],{},[706,3964],{"width":2564},[598,3966,2567],{},[706,3968],{"width":2564},[594,3970,942],{},[598,3972,612],{"stretchy":611},[594,3974,615],{},[598,3976,618],{"stretchy":611},[598,3978,627],{},[594,3980,615],{},[706,3982],{"width":2564},[598,3984,2567],{},[706,3986],{"width":2564},[931,3988,3989,3991],{},[594,3990,596],{},[594,3992,564],{},[598,3994,627],{},[594,3996,615],{},[620,3998,622],{},[591,4000,4001,4003],{},[594,4002,949],{},[588,4004,4005,4007,4009],{},[598,4006,954],{},[818,4008,3533],{},[594,4010,615],{},[638,4012,4013],{"encoding":640},"C'(x) = e^{-2x} \\cdot e^{2x} = 1 \\quad\\Rightarrow\\quad C(x) = x \\quad\\Rightarrow\\quad y_p = x\\,e^{-2x}",[572,4015,4017,4073,4127,4177,4201,4228,4252,4307],{"className":4016,"ariaHidden":646},[645],[572,4018,4020,4023,4055,4058,4061,4064,4067,4070],{"className":4019},[650],[572,4021],{"className":4022,"style":2650},[654],[572,4024,4026,4029],{"className":4025},[659],[572,4027,942],{"className":4028,"style":1042},[659,663],[572,4030,4032],{"className":4031},[668],[572,4033,4035],{"className":4034},[672],[572,4036,4038],{"className":4037},[676],[572,4039,4041],{"className":4040,"style":2669},[680],[572,4042,4043,4046],{"style":2672},[572,4044],{"className":4045,"style":689},[688],[572,4047,4049],{"className":4048},[693,694,695,696],[572,4050,4052],{"className":4051},[659,696],[572,4053,602],{"className":4054},[659,696],[572,4056,612],{"className":4057},[728],[572,4059,615],{"className":4060},[659,663],[572,4062,618],{"className":4063},[735],[572,4065],{"className":4066,"style":746},[706],[572,4068,627],{"className":4069},[750],[572,4071],{"className":4072,"style":746},[706],[572,4074,4076,4080,4118,4121,4124],{"className":4075},[650],[572,4077],{"className":4078,"style":4079},[654],"height:0.8641em;",[572,4081,4083,4086],{"className":4082},[659],[572,4084,949],{"className":4085},[659,663],[572,4087,4089],{"className":4088},[668],[572,4090,4092],{"className":4091},[672],[572,4093,4095],{"className":4094},[676],[572,4096,4098],{"className":4097,"style":4079},[680],[572,4099,4100,4103],{"style":2672},[572,4101],{"className":4102,"style":689},[688],[572,4104,4106],{"className":4105},[693,694,695,696],[572,4107,4109,4112,4115],{"className":4108},[659,696],[572,4110,954],{"className":4111},[659,696],[572,4113,3533],{"className":4114},[659,696],[572,4116,615],{"className":4117},[659,663,696],[572,4119],{"className":4120,"style":707},[706],[572,4122,3948],{"className":4123},[711],[572,4125],{"className":4126,"style":707},[706],[572,4128,4130,4133,4168,4171,4174],{"className":4129},[650],[572,4131],{"className":4132,"style":4079},[654],[572,4134,4136,4139],{"className":4135},[659],[572,4137,949],{"className":4138},[659,663],[572,4140,4142],{"className":4141},[668],[572,4143,4145],{"className":4144},[672],[572,4146,4148],{"className":4147},[676],[572,4149,4151],{"className":4150,"style":4079},[680],[572,4152,4153,4156],{"style":2672},[572,4154],{"className":4155,"style":689},[688],[572,4157,4159],{"className":4158},[693,694,695,696],[572,4160,4162,4165],{"className":4161},[659,696],[572,4163,3533],{"className":4164},[659,696],[572,4166,615],{"className":4167},[659,663,696],[572,4169],{"className":4170,"style":746},[706],[572,4172,627],{"className":4173},[750],[572,4175],{"className":4176,"style":746},[706],[572,4178,4180,4183,4186,4189,4192,4195,4198],{"className":4179},[650],[572,4181],{"className":4182,"style":913},[654],[572,4184,2120],{"className":4185},[659],[572,4187],{"className":4188,"style":2751},[706],[572,4190],{"className":4191,"style":746},[706],[572,4193,2567],{"className":4194},[750],[572,4196],{"className":4197,"style":2751},[706],[572,4199],{"className":4200,"style":746},[706],[572,4202,4204,4207,4210,4213,4216,4219,4222,4225],{"className":4203},[650],[572,4205],{"className":4206,"style":721},[654],[572,4208,942],{"className":4209,"style":1042},[659,663],[572,4211,612],{"className":4212},[728],[572,4214,615],{"className":4215},[659,663],[572,4217,618],{"className":4218},[735],[572,4220],{"className":4221,"style":746},[706],[572,4223,627],{"className":4224},[750],[572,4226],{"className":4227,"style":746},[706],[572,4229,4231,4234,4237,4240,4243,4246,4249],{"className":4230},[650],[572,4232],{"className":4233,"style":2095},[654],[572,4235,615],{"className":4236},[659,663],[572,4238],{"className":4239,"style":2751},[706],[572,4241],{"className":4242,"style":746},[706],[572,4244,2567],{"className":4245},[750],[572,4247],{"className":4248,"style":2751},[706],[572,4250],{"className":4251,"style":746},[706],[572,4253,4255,4258,4298,4301,4304],{"className":4254},[650],[572,4256],{"className":4257,"style":1152},[654],[572,4259,4261,4264],{"className":4260},[659],[572,4262,596],{"className":4263,"style":664},[659,663],[572,4265,4267],{"className":4266},[668],[572,4268,4270,4290],{"className":4269},[672,989],[572,4271,4273,4287],{"className":4272},[676],[572,4274,4276],{"className":4275,"style":1171},[680],[572,4277,4278,4281],{"style":999},[572,4279],{"className":4280,"style":689},[688],[572,4282,4284],{"className":4283},[693,694,695,696],[572,4285,564],{"className":4286},[659,663,696],[572,4288,1013],{"className":4289},[1012],[572,4291,4293],{"className":4292},[676],[572,4294,4296],{"className":4295,"style":1192},[680],[572,4297],{},[572,4299],{"className":4300,"style":746},[706],[572,4302,627],{"className":4303},[750],[572,4305],{"className":4306,"style":746},[706],[572,4308,4310,4313,4316,4319],{"className":4309},[650],[572,4311],{"className":4312,"style":4079},[654],[572,4314,615],{"className":4315},[659,663],[572,4317],{"className":4318,"style":739},[706],[572,4320,4322,4325],{"className":4321},[659],[572,4323,949],{"className":4324},[659,663],[572,4326,4328],{"className":4327},[668],[572,4329,4331],{"className":4330},[672],[572,4332,4334],{"className":4333},[676],[572,4335,4337],{"className":4336,"style":4079},[680],[572,4338,4339,4342],{"style":2672},[572,4340],{"className":4341,"style":689},[688],[572,4343,4345],{"className":4344},[693,694,695,696],[572,4346,4348,4351,4354],{"className":4347},[659,696],[572,4349,954],{"className":4350},[659,696],[572,4352,3533],{"className":4353},[659,696],[572,4355,615],{"className":4356},[659,663,696],[564,4358,3263,4359,1090],{},[572,4360,4362,4460],{"className":4361},[575],[572,4363,4365],{"className":4364},[579],[581,4366,4367],{"xmlns":583},[585,4368,4369,4457],{},[588,4370,4371,4379,4381,4383,4389,4391,4403,4405,4407,4409,4411,4423,4425,4427,4429,4431,4443,4445],{},[1893,4372,4373,4375,4377],{},[594,4374,596],{},[594,4376,564],{},[598,4378,602],{"mathvariant":600,"lspace":601,"rspace":601},[598,4380,605],{},[818,4382,3533],{},[931,4384,4385,4387],{},[594,4386,596],{},[594,4388,564],{},[598,4390,627],{},[591,4392,4393,4395],{},[594,4394,949],{},[588,4396,4397,4399,4401],{},[598,4398,954],{},[818,4400,3533],{},[594,4402,615],{},[598,4404,954],{},[818,4406,3533],{},[594,4408,615],{},[620,4410,622],{},[591,4412,4413,4415],{},[594,4414,949],{},[588,4416,4417,4419,4421],{},[598,4418,954],{},[818,4420,3533],{},[594,4422,615],{},[598,4424,605],{},[818,4426,3533],{},[594,4428,615],{},[620,4430,622],{},[591,4432,4433,4435],{},[594,4434,949],{},[588,4436,4437,4439,4441],{},[598,4438,954],{},[818,4440,3533],{},[594,4442,615],{},[598,4444,627],{},[591,4446,4447,4449],{},[594,4448,949],{},[588,4450,4451,4453,4455],{},[598,4452,954],{},[818,4454,3533],{},[594,4456,615],{},[638,4458,4459],{"encoding":640},"y_p' + 2y_p = e^{-2x} - 2x\\,e^{-2x} + 2x\\,e^{-2x} = e^{-2x}",[572,4461,4463,4532,4591,4645,4707,4769],{"className":4462,"ariaHidden":646},[645],[572,4464,4466,4469,4523,4526,4529],{"className":4465},[650],[572,4467],{"className":4468,"style":3322},[654],[572,4470,4472,4475],{"className":4471},[659],[572,4473,596],{"className":4474,"style":664},[659,663],[572,4476,4478],{"className":4477},[668],[572,4479,4481,4515],{"className":4480},[672,989],[572,4482,4484,4512],{"className":4483},[676],[572,4485,4487,4498],{"className":4486,"style":681},[680],[572,4488,4489,4492],{"style":3343},[572,4490],{"className":4491,"style":689},[688],[572,4493,4495],{"className":4494},[693,694,695,696],[572,4496,564],{"className":4497},[659,663,696],[572,4499,4500,4503],{"style":684},[572,4501],{"className":4502,"style":689},[688],[572,4504,4506],{"className":4505},[693,694,695,696],[572,4507,4509],{"className":4508},[659,696],[572,4510,602],{"className":4511},[659,696],[572,4513,1013],{"className":4514},[1012],[572,4516,4518],{"className":4517},[676],[572,4519,4521],{"className":4520,"style":3376},[680],[572,4522],{},[572,4524],{"className":4525,"style":707},[706],[572,4527,605],{"className":4528},[711],[572,4530],{"className":4531,"style":707},[706],[572,4533,4535,4539,4542,4582,4585,4588],{"className":4534},[650],[572,4536],{"className":4537,"style":4538},[654],"height:0.9305em;vertical-align:-0.2861em;",[572,4540,3533],{"className":4541},[659],[572,4543,4545,4548],{"className":4544},[659],[572,4546,596],{"className":4547,"style":664},[659,663],[572,4549,4551],{"className":4550},[668],[572,4552,4554,4574],{"className":4553},[672,989],[572,4555,4557,4571],{"className":4556},[676],[572,4558,4560],{"className":4559,"style":1171},[680],[572,4561,4562,4565],{"style":999},[572,4563],{"className":4564,"style":689},[688],[572,4566,4568],{"className":4567},[693,694,695,696],[572,4569,564],{"className":4570},[659,663,696],[572,4572,1013],{"className":4573},[1012],[572,4575,4577],{"className":4576},[676],[572,4578,4580],{"className":4579,"style":1192},[680],[572,4581],{},[572,4583],{"className":4584,"style":746},[706],[572,4586,627],{"className":4587},[750],[572,4589],{"className":4590,"style":746},[706],[572,4592,4594,4598,4636,4639,4642],{"className":4593},[650],[572,4595],{"className":4596,"style":4597},[654],"height:0.8974em;vertical-align:-0.0833em;",[572,4599,4601,4604],{"className":4600},[659],[572,4602,949],{"className":4603},[659,663],[572,4605,4607],{"className":4606},[668],[572,4608,4610],{"className":4609},[672],[572,4611,4613],{"className":4612},[676],[572,4614,4616],{"className":4615,"style":3631},[680],[572,4617,4618,4621],{"style":684},[572,4619],{"className":4620,"style":689},[688],[572,4622,4624],{"className":4623},[693,694,695,696],[572,4625,4627,4630,4633],{"className":4626},[659,696],[572,4628,954],{"className":4629},[659,696],[572,4631,3533],{"className":4632},[659,696],[572,4634,615],{"className":4635},[659,663,696],[572,4637],{"className":4638,"style":707},[706],[572,4640,954],{"className":4641},[711],[572,4643],{"className":4644,"style":707},[706],[572,4646,4648,4651,4654,4657,4660,4698,4701,4704],{"className":4647},[650],[572,4649],{"className":4650,"style":4597},[654],[572,4652,3533],{"className":4653},[659],[572,4655,615],{"className":4656},[659,663],[572,4658],{"className":4659,"style":739},[706],[572,4661,4663,4666],{"className":4662},[659],[572,4664,949],{"className":4665},[659,663],[572,4667,4669],{"className":4668},[668],[572,4670,4672],{"className":4671},[672],[572,4673,4675],{"className":4674},[676],[572,4676,4678],{"className":4677,"style":3631},[680],[572,4679,4680,4683],{"style":684},[572,4681],{"className":4682,"style":689},[688],[572,4684,4686],{"className":4685},[693,694,695,696],[572,4687,4689,4692,4695],{"className":4688},[659,696],[572,4690,954],{"className":4691},[659,696],[572,4693,3533],{"className":4694},[659,696],[572,4696,615],{"className":4697},[659,663,696],[572,4699],{"className":4700,"style":707},[706],[572,4702,605],{"className":4703},[711],[572,4705],{"className":4706,"style":707},[706],[572,4708,4710,4713,4716,4719,4722,4760,4763,4766],{"className":4709},[650],[572,4711],{"className":4712,"style":3631},[654],[572,4714,3533],{"className":4715},[659],[572,4717,615],{"className":4718},[659,663],[572,4720],{"className":4721,"style":739},[706],[572,4723,4725,4728],{"className":4724},[659],[572,4726,949],{"className":4727},[659,663],[572,4729,4731],{"className":4730},[668],[572,4732,4734],{"className":4733},[672],[572,4735,4737],{"className":4736},[676],[572,4738,4740],{"className":4739,"style":3631},[680],[572,4741,4742,4745],{"style":684},[572,4743],{"className":4744,"style":689},[688],[572,4746,4748],{"className":4747},[693,694,695,696],[572,4749,4751,4754,4757],{"className":4750},[659,696],[572,4752,954],{"className":4753},[659,696],[572,4755,3533],{"className":4756},[659,696],[572,4758,615],{"className":4759},[659,663,696],[572,4761],{"className":4762,"style":746},[706],[572,4764,627],{"className":4765},[750],[572,4767],{"className":4768,"style":746},[706],[572,4770,4772,4775],{"className":4771},[650],[572,4773],{"className":4774,"style":3631},[654],[572,4776,4778,4781],{"className":4777},[659],[572,4779,949],{"className":4780},[659,663],[572,4782,4784],{"className":4783},[668],[572,4785,4787],{"className":4786},[672],[572,4788,4790],{"className":4789},[676],[572,4791,4793],{"className":4792,"style":3631},[680],[572,4794,4795,4798],{"style":684},[572,4796],{"className":4797,"style":689},[688],[572,4799,4801],{"className":4800},[693,694,695,696],[572,4802,4804,4807,4810],{"className":4803},[659,696],[572,4805,954],{"className":4806},[659,696],[572,4808,3533],{"className":4809},[659,696],[572,4811,615],{"className":4812},[659,663,696],[559,4814,4816],{"id":4815},"typische-fehler","Typische Fehler",[4818,4819,4820,5187,5479,5686],"ul",{},[777,4821,4822,4823,4866,4867,1090],{},"Beim Einsetzen nicht beachten, dass ",[572,4824,4826,4845],{"className":4825},[575],[572,4827,4829],{"className":4828},[579],[581,4830,4831],{"xmlns":583},[585,4832,4833,4843],{},[588,4834,4835,4837,4839,4841],{},[594,4836,942],{},[598,4838,612],{"stretchy":611},[594,4840,615],{},[598,4842,618],{"stretchy":611},[638,4844,1295],{"encoding":640},[572,4846,4848],{"className":4847,"ariaHidden":646},[645],[572,4849,4851,4854,4857,4860,4863],{"className":4850},[650],[572,4852],{"className":4853,"style":721},[654],[572,4855,942],{"className":4856,"style":1042},[659,663],[572,4858,612],{"className":4859},[728],[572,4861,615],{"className":4862},[659,663],[572,4864,618],{"className":4865},[735]," jetzt abgeleitet werden muss: ",[572,4868,4870,4948],{"className":4869},[575],[572,4871,4873],{"className":4872},[579],[581,4874,4875],{"xmlns":583},[585,4876,4877,4945],{},[588,4878,4879,4887,4889,4895,4897,4899,4901,4903,4913,4915,4917,4919,4921,4923,4925,4927,4929,4931,4933,4935],{},[1893,4880,4881,4883,4885],{},[594,4882,596],{},[594,4884,564],{},[598,4886,602],{"mathvariant":600,"lspace":601,"rspace":601},[598,4888,627],{},[591,4890,4891,4893],{},[594,4892,942],{},[598,4894,602],{"mathvariant":600,"lspace":601,"rspace":601},[598,4896,612],{"stretchy":611},[594,4898,615],{},[598,4900,618],{"stretchy":611},[620,4902,622],{},[591,4904,4905,4907],{},[594,4906,949],{},[588,4908,4909,4911],{},[598,4910,954],{},[594,4912,957],{},[598,4914,954],{},[594,4916,608],{},[598,4918,612],{"stretchy":611},[594,4920,615],{},[598,4922,618],{"stretchy":611},[620,4924,622],{},[594,4926,942],{},[598,4928,612],{"stretchy":611},[594,4930,615],{},[598,4932,618],{"stretchy":611},[620,4934,622],{},[591,4936,4937,4939],{},[594,4938,949],{},[588,4940,4941,4943],{},[598,4942,954],{},[594,4944,957],{},[638,4946,4947],{"encoding":640},"y_p' = C'(x)\\,e^{-A} - a(x)\\,C(x)\\,e^{-A}",[572,4949,4951,5020,5116],{"className":4950,"ariaHidden":646},[645],[572,4952,4954,4957,5011,5014,5017],{"className":4953},[650],[572,4955],{"className":4956,"style":3322},[654],[572,4958,4960,4963],{"className":4959},[659],[572,4961,596],{"className":4962,"style":664},[659,663],[572,4964,4966],{"className":4965},[668],[572,4967,4969,5003],{"className":4968},[672,989],[572,4970,4972,5000],{"className":4971},[676],[572,4973,4975,4986],{"className":4974,"style":681},[680],[572,4976,4977,4980],{"style":3343},[572,4978],{"className":4979,"style":689},[688],[572,4981,4983],{"className":4982},[693,694,695,696],[572,4984,564],{"className":4985},[659,663,696],[572,4987,4988,4991],{"style":684},[572,4989],{"className":4990,"style":689},[688],[572,4992,4994],{"className":4993},[693,694,695,696],[572,4995,4997],{"className":4996},[659,696],[572,4998,602],{"className":4999},[659,696],[572,5001,1013],{"className":5002},[1012],[572,5004,5006],{"className":5005},[676],[572,5007,5009],{"className":5008,"style":3376},[680],[572,5010],{},[572,5012],{"className":5013,"style":746},[706],[572,5015,627],{"className":5016},[750],[572,5018],{"className":5019,"style":746},[706],[572,5021,5023,5027,5059,5062,5065,5068,5071,5107,5110,5113],{"className":5022},[650],[572,5024],{"className":5025,"style":5026},[654],"height:1.0913em;vertical-align:-0.25em;",[572,5028,5030,5033],{"className":5029},[659],[572,5031,942],{"className":5032,"style":1042},[659,663],[572,5034,5036],{"className":5035},[668],[572,5037,5039],{"className":5038},[672],[572,5040,5042],{"className":5041},[676],[572,5043,5045],{"className":5044,"style":681},[680],[572,5046,5047,5050],{"style":684},[572,5048],{"className":5049,"style":689},[688],[572,5051,5053],{"className":5052},[693,694,695,696],[572,5054,5056],{"className":5055},[659,696],[572,5057,602],{"className":5058},[659,696],[572,5060,612],{"className":5061},[728],[572,5063,615],{"className":5064},[659,663],[572,5066,618],{"className":5067},[735],[572,5069],{"className":5070,"style":739},[706],[572,5072,5074,5077],{"className":5073},[659],[572,5075,949],{"className":5076},[659,663],[572,5078,5080],{"className":5079},[668],[572,5081,5083],{"className":5082},[672],[572,5084,5086],{"className":5085},[676],[572,5087,5090],{"className":5088,"style":5089},[680],"height:0.8413em;",[572,5091,5092,5095],{"style":684},[572,5093],{"className":5094,"style":689},[688],[572,5096,5098],{"className":5097},[693,694,695,696],[572,5099,5101,5104],{"className":5100},[659,696],[572,5102,954],{"className":5103},[659,696],[572,5105,957],{"className":5106},[659,663,696],[572,5108],{"className":5109,"style":707},[706],[572,5111,954],{"className":5112},[711],[572,5114],{"className":5115,"style":707},[706],[572,5117,5119,5122,5125,5128,5131,5134,5137,5140,5143,5146,5149,5152],{"className":5118},[650],[572,5120],{"className":5121,"style":5026},[654],[572,5123,608],{"className":5124},[659,663],[572,5126,612],{"className":5127},[728],[572,5129,615],{"className":5130},[659,663],[572,5132,618],{"className":5133},[735],[572,5135],{"className":5136,"style":739},[706],[572,5138,942],{"className":5139,"style":1042},[659,663],[572,5141,612],{"className":5142},[728],[572,5144,615],{"className":5145},[659,663],[572,5147,618],{"className":5148},[735],[572,5150],{"className":5151,"style":739},[706],[572,5153,5155,5158],{"className":5154},[659],[572,5156,949],{"className":5157},[659,663],[572,5159,5161],{"className":5160},[668],[572,5162,5164],{"className":5163},[672],[572,5165,5167],{"className":5166},[676],[572,5168,5170],{"className":5169,"style":5089},[680],[572,5171,5172,5175],{"style":684},[572,5173],{"className":5174,"style":689},[688],[572,5176,5178],{"className":5177},[693,694,695,696],[572,5179,5181,5184],{"className":5180},[659,696],[572,5182,954],{"className":5183},[659,696],[572,5185,957],{"className":5186},[659,663,696],[777,5188,5189,5368,5369,5478],{},[572,5190,5192,5244],{"className":5191},[575],[572,5193,5195],{"className":5194},[579],[581,5196,5197],{"xmlns":583},[585,5198,5199,5241],{},[588,5200,5201,5207,5209,5211,5213,5215,5217,5219,5221,5223,5225],{},[591,5202,5203,5205],{},[594,5204,942],{},[598,5206,602],{"mathvariant":600,"lspace":601,"rspace":601},[598,5208,612],{"stretchy":611},[594,5210,615],{},[598,5212,618],{"stretchy":611},[598,5214,627],{},[594,5216,630],{},[598,5218,612],{"stretchy":611},[594,5220,615],{},[598,5222,618],{"stretchy":611},[620,5224,622],{},[591,5226,5227,5229],{},[594,5228,949],{},[588,5230,5231,5233,5235,5237,5239],{},[598,5232,954],{},[594,5234,957],{},[598,5236,612],{"stretchy":611},[594,5238,615],{},[598,5240,618],{"stretchy":611},[638,5242,5243],{"encoding":640},"C'(x) = b(x)\\,e^{-A(x)}",[572,5245,5247,5303],{"className":5246,"ariaHidden":646},[645],[572,5248,5250,5253,5285,5288,5291,5294,5297,5300],{"className":5249},[650],[572,5251],{"className":5252,"style":1560},[654],[572,5254,5256,5259],{"className":5255},[659],[572,5257,942],{"className":5258,"style":1042},[659,663],[572,5260,5262],{"className":5261},[668],[572,5263,5265],{"className":5264},[672],[572,5266,5268],{"className":5267},[676],[572,5269,5271],{"className":5270,"style":681},[680],[572,5272,5273,5276],{"style":684},[572,5274],{"className":5275,"style":689},[688],[572,5277,5279],{"className":5278},[693,694,695,696],[572,5280,5282],{"className":5281},[659,696],[572,5283,602],{"className":5284},[659,696],[572,5286,612],{"className":5287},[728],[572,5289,615],{"className":5290},[659,663],[572,5292,618],{"className":5293},[735],[572,5295],{"className":5296,"style":746},[706],[572,5298,627],{"className":5299},[750],[572,5301],{"className":5302,"style":746},[706],[572,5304,5306,5309,5312,5315,5318,5321,5324],{"className":5305},[650],[572,5307],{"className":5308,"style":1210},[654],[572,5310,630],{"className":5311},[659,663],[572,5313,612],{"className":5314},[728],[572,5316,615],{"className":5317},[659,663],[572,5319,618],{"className":5320},[735],[572,5322],{"className":5323,"style":739},[706],[572,5325,5327,5330],{"className":5326},[659],[572,5328,949],{"className":5329},[659,663],[572,5331,5333],{"className":5332},[668],[572,5334,5336],{"className":5335},[672],[572,5337,5339],{"className":5338},[676],[572,5340,5342],{"className":5341,"style":1038},[680],[572,5343,5344,5347],{"style":684},[572,5345],{"className":5346,"style":689},[688],[572,5348,5350],{"className":5349},[693,694,695,696],[572,5351,5353,5356,5359,5362,5365],{"className":5352},[659,696],[572,5354,954],{"className":5355},[659,696],[572,5357,957],{"className":5358},[659,663,696],[572,5360,612],{"className":5361},[728,696],[572,5363,615],{"className":5364},[659,663,696],[572,5366,618],{"className":5367},[735,696]," statt ",[572,5370,5372,5410],{"className":5371},[575],[572,5373,5375],{"className":5374},[579],[581,5376,5377],{"xmlns":583},[585,5378,5379,5407],{},[588,5380,5381,5383,5385,5387,5389,5391],{},[594,5382,630],{},[598,5384,612],{"stretchy":611},[594,5386,615],{},[598,5388,618],{"stretchy":611},[620,5390,622],{},[591,5392,5393,5395],{},[594,5394,949],{},[588,5396,5397,5399,5401,5403,5405],{},[598,5398,605],{},[594,5400,957],{},[598,5402,612],{"stretchy":611},[594,5404,615],{},[598,5406,618],{"stretchy":611},[638,5408,5409],{"encoding":640},"b(x)\\,e^{+A(x)}",[572,5411,5413],{"className":5412,"ariaHidden":646},[645],[572,5414,5416,5419,5422,5425,5428,5431,5434],{"className":5415},[650],[572,5417],{"className":5418,"style":1210},[654],[572,5420,630],{"className":5421},[659,663],[572,5423,612],{"className":5424},[728],[572,5426,615],{"className":5427},[659,663],[572,5429,618],{"className":5430},[735],[572,5432],{"className":5433,"style":739},[706],[572,5435,5437,5440],{"className":5436},[659],[572,5438,949],{"className":5439},[659,663],[572,5441,5443],{"className":5442},[668],[572,5444,5446],{"className":5445},[672],[572,5447,5449],{"className":5448},[676],[572,5450,5452],{"className":5451,"style":1038},[680],[572,5453,5454,5457],{"style":684},[572,5455],{"className":5456,"style":689},[688],[572,5458,5460],{"className":5459},[693,694,695,696],[572,5461,5463,5466,5469,5472,5475],{"className":5462},[659,696],[572,5464,605],{"className":5465},[659,696],[572,5467,957],{"className":5468},[659,663,696],[572,5470,612],{"className":5471},[728,696],[572,5473,615],{"className":5474},[659,663,696],[572,5476,618],{"className":5477},[735,696]," schreiben.",[777,5480,5481,5482,5615,5616,1090],{},"Am Ende die homogene Lösung vergessen: Die allgemeine Lösung ist ",[572,5483,5485,5511],{"className":5484},[575],[572,5486,5488],{"className":5487},[579],[581,5489,5490],{"xmlns":583},[585,5491,5492,5508],{},[588,5493,5494,5500,5502],{},[931,5495,5496,5498],{},[594,5497,596],{},[594,5499,937],{},[598,5501,605],{},[931,5503,5504,5506],{},[594,5505,596],{},[594,5507,564],{},[638,5509,5510],{"encoding":640},"y_h + y_p",[572,5512,5514,5569],{"className":5513,"ariaHidden":646},[645],[572,5515,5517,5520,5560,5563,5566],{"className":5516},[650],[572,5518],{"className":5519,"style":1780},[654],[572,5521,5523,5526],{"className":5522},[659],[572,5524,596],{"className":5525,"style":664},[659,663],[572,5527,5529],{"className":5528},[668],[572,5530,5532,5552],{"className":5531},[672,989],[572,5533,5535,5549],{"className":5534},[676],[572,5536,5538],{"className":5537,"style":996},[680],[572,5539,5540,5543],{"style":999},[572,5541],{"className":5542,"style":689},[688],[572,5544,5546],{"className":5545},[693,694,695,696],[572,5547,937],{"className":5548},[659,663,696],[572,5550,1013],{"className":5551},[1012],[572,5553,5555],{"className":5554},[676],[572,5556,5558],{"className":5557,"style":1020},[680],[572,5559],{},[572,5561],{"className":5562,"style":707},[706],[572,5564,605],{"className":5565},[711],[572,5567],{"className":5568,"style":707},[706],[572,5570,5572,5575],{"className":5571},[650],[572,5573],{"className":5574,"style":1152},[654],[572,5576,5578,5581],{"className":5577},[659],[572,5579,596],{"className":5580,"style":664},[659,663],[572,5582,5584],{"className":5583},[668],[572,5585,5587,5607],{"className":5586},[672,989],[572,5588,5590,5604],{"className":5589},[676],[572,5591,5593],{"className":5592,"style":1171},[680],[572,5594,5595,5598],{"style":999},[572,5596],{"className":5597,"style":689},[688],[572,5599,5601],{"className":5600},[693,694,695,696],[572,5602,564],{"className":5603},[659,663,696],[572,5605,1013],{"className":5606},[1012],[572,5608,5610],{"className":5609},[676],[572,5611,5613],{"className":5612,"style":1192},[680],[572,5614],{},", nicht nur ",[572,5617,5619,5637],{"className":5618},[575],[572,5620,5622],{"className":5621},[579],[581,5623,5624],{"xmlns":583},[585,5625,5626,5634],{},[588,5627,5628],{},[931,5629,5630,5632],{},[594,5631,596],{},[594,5633,564],{},[638,5635,5636],{"encoding":640},"y_p",[572,5638,5640],{"className":5639,"ariaHidden":646},[645],[572,5641,5643,5646],{"className":5642},[650],[572,5644],{"className":5645,"style":1152},[654],[572,5647,5649,5652],{"className":5648},[659],[572,5650,596],{"className":5651,"style":664},[659,663],[572,5653,5655],{"className":5654},[668],[572,5656,5658,5678],{"className":5657},[672,989],[572,5659,5661,5675],{"className":5660},[676],[572,5662,5664],{"className":5663,"style":1171},[680],[572,5665,5666,5669],{"style":999},[572,5667],{"className":5668,"style":689},[688],[572,5670,5672],{"className":5671},[693,694,695,696],[572,5673,564],{"className":5674},[659,663,696],[572,5676,1013],{"className":5677},[1012],[572,5679,5681],{"className":5680},[676],[572,5682,5684],{"className":5683,"style":1192},[680],[572,5685],{},[777,5687,5688,5689,5717,5718,5780,5781,5825],{},"Die Gleichung nicht auf Normalform mit Faktor ",[572,5690,5692,5705],{"className":5691},[575],[572,5693,5695],{"className":5694},[579],[581,5696,5697],{"xmlns":583},[585,5698,5699,5703],{},[588,5700,5701],{},[818,5702,2120],{},[638,5704,2120],{"encoding":640},[572,5706,5708],{"className":5707,"ariaHidden":646},[645],[572,5709,5711,5714],{"className":5710},[650],[572,5712],{"className":5713,"style":913},[654],[572,5715,2120],{"className":5716},[659]," vor ",[572,5719,5721,5739],{"className":5720},[575],[572,5722,5724],{"className":5723},[579],[581,5725,5726],{"xmlns":583},[585,5727,5728,5736],{},[588,5729,5730],{},[591,5731,5732,5734],{},[594,5733,596],{},[598,5735,602],{"mathvariant":600,"lspace":601,"rspace":601},[638,5737,5738],{"encoding":640},"y'",[572,5740,5742],{"className":5741,"ariaHidden":646},[645],[572,5743,5745,5748],{"className":5744},[650],[572,5746],{"className":5747,"style":655},[654],[572,5749,5751,5754],{"className":5750},[659],[572,5752,596],{"className":5753,"style":664},[659,663],[572,5755,5757],{"className":5756},[668],[572,5758,5760],{"className":5759},[672],[572,5761,5763],{"className":5762},[676],[572,5764,5766],{"className":5765,"style":681},[680],[572,5767,5768,5771],{"style":684},[572,5769],{"className":5770,"style":689},[688],[572,5772,5774],{"className":5773},[693,694,695,696],[572,5775,5777],{"className":5776},[659,696],[572,5778,602],{"className":5779},[659,696]," bringen, bevor man ",[572,5782,5784,5804],{"className":5783},[575],[572,5785,5787],{"className":5786},[579],[581,5788,5789],{"xmlns":583},[585,5790,5791,5801],{},[588,5792,5793,5795,5797,5799],{},[594,5794,630],{},[598,5796,612],{"stretchy":611},[594,5798,615],{},[598,5800,618],{"stretchy":611},[638,5802,5803],{"encoding":640},"b(x)",[572,5805,5807],{"className":5806,"ariaHidden":646},[645],[572,5808,5810,5813,5816,5819,5822],{"className":5809},[650],[572,5811],{"className":5812,"style":721},[654],[572,5814,630],{"className":5815},[659,663],[572,5817,612],{"className":5818},[728],[572,5820,615],{"className":5821},[659,663],[572,5823,618],{"className":5824},[735]," abliest.",{"title":5827,"searchDepth":5828,"depth":5828,"links":5829},"",2,[5830,5831,5832],{"id":561,"depth":5828,"text":562},{"id":1988,"depth":5828,"text":1989},{"id":4815,"depth":5828,"text":4816},[5834,5837,5840,5843,5845,5847,5849],{"lhs":5835,"rhs":5836},"(3*x*exp(2*x))*exp(-2*x)","3*x",{"lhs":5838,"rhs":5839},"-exp(-x) + (x + 1)*exp(-x)","x*exp(-x)",{"lhs":5841,"rhs":5842},"-(x + 1)*exp(-x)*exp(x)","-(x + 1)",{"lhs":5844,"rhs":615},"-1 - (-(x + 1))",{"lhs":5846,"rhs":615},"(K*exp(x) - 1) - (K*exp(x) - x - 1)",{"lhs":5848,"rhs":2120},"exp(-2*x)*exp(2*x)",{"lhs":5850,"rhs":5851},"(exp(-2*x) - 2*x*exp(-2*x)) + 2*x*exp(-2*x)","exp(-2*x)","y' + a(x)\\,y = b(x),\\ A'(x) = a(x)","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsup>\u003Cmi>y\u003C\u002Fmi>\u003Cmo mathvariant=\"normal\" lspace=\"0em\" rspace=\"0em\">′\u003C\u002Fmo>\u003C\u002Fmsup>\u003Cmo>+\u003C\u002Fmo>\u003Cmi>a\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmtext> \u003C\u002Fmtext>\u003Cmi>y\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmo 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class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsup>\u003Cmi>A\u003C\u002Fmi>\u003Cmo mathvariant=\"normal\" lspace=\"0em\" rspace=\"0em\">′\u003C\u002Fmo>\u003C\u002Fmsup>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>=\u003C\u002Fmo>\u003Cmi>a\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">A'(x) = a(x)\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1.0019em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.7519em;\">\u003Cspan style=\"top:-3.063em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mtight\">′\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","variation-of-constants","y_p(x) = C(x)\\,e^{-A(x)}, \\qquad C'(x) = b(x)\\,e^{A(x)}","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>y\u003C\u002Fmi>\u003Cmi>p\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>=\u003C\u002Fmo>\u003Cmi>C\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmtext> \u003C\u002Fmtext>\u003Cmsup>\u003Cmi>e\u003C\u002Fmi>\u003Cmrow>\u003Cmo>−\u003C\u002Fmo>\u003Cmi>A\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003C\u002Fmsup>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmspace width=\"2em\"\u002F>\u003Cmsup>\u003Cmi>C\u003C\u002Fmi>\u003Cmo mathvariant=\"normal\" lspace=\"0em\" rspace=\"0em\">′\u003C\u002Fmo>\u003C\u002Fmsup>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>=\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmtext> \u003C\u002Fmtext>\u003Cmsup>\u003Cmi>e\u003C\u002Fmi>\u003Cmrow>\u003Cmi>A\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003C\u002Fmsup>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">y_p(x) = C(x)\\,e^{-A(x)}, \\qquad C'(x) = b(x)\\,e^{A(x)}\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1.0361em;vertical-align:-0.2861em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">y\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.1514em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\">p\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.2861em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord 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style=\"top:-3.113em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mtight\">−\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal mtight\">A\u003C\u002Fspan>\u003Cspan class=\"mopen mtight\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal mtight\">x\u003C\u002Fspan>\u003Cspan class=\"mclose mtight\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:2em;\">\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0715em;\">C\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8019em;\">\u003Cspan style=\"top:-3.113em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mtight\">′\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1.188em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">e\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.938em;\">\u003Cspan style=\"top:-3.113em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\">A\u003C\u002Fspan>\u003Cspan class=\"mopen mtight\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal mtight\">x\u003C\u002Fspan>\u003Cspan class=\"mclose mtight\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","university",{},true,"\u002Fde\u002Fformulas\u002Fmath\u002Fdifferential-equations\u002Fvariation-der-konstanten",[],[5865,5866,5867],"linear-ode-first-order","characteristic-equation","integration-by-parts",{"title":548,"description":5827},"de\u002Fformulas\u002Fmath\u002Fdifferential-equations\u002Fvariation-der-konstanten","Man ersetzt die Konstante der homogenen Lösung durch eine Funktion C(x) und erhält so eine Lösung der inhomogenen Gleichung.",[5872,5873,5874,5875],"differentialgleichung","partikuläre lösung","inhomogene dgl","lineare dgl",[5877,5880,5883,5887,5891],{"symbol":5636,"meaning":5878,"symbolHtml":5879},"partikuläre (spezielle) Lösung der inhomogenen Gleichung","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath 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class=\"mord mathnormal mtight\">p\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.2861em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":1295,"meaning":5881,"symbolHtml":5882},"Funktion, die an die Stelle der Konstanten C der homogenen Lösung tritt","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>C\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation 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