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Produkts:",[573,1145,1147],{"className":1146},[798],[573,1148,1150,1215],{"className":1149},[576],[573,1151,1153],{"className":1152},[580],[582,1154,1155],{"xmlns":584,"display":807},[586,1156,1157,1212],{},[589,1158,1159,1162,1164,1166,1180,1186,1188,1190,1192,1194,1196,1198],{},[638,1160,827],{"fence":603,"stretchy":603,"minsize":1161,"maxsize":1161},"1.2em",[592,1163,594],{},[835,1165,837],{},[633,1167,1168,1170],{},[592,1169,991],{},[589,1171,1172,1174,1176,1178],{},[592,1173,996],{},[638,1175,827],{"stretchy":826},[592,1177,830],{},[638,1179,833],{"stretchy":826},[633,1181,1182,1184],{},[638,1183,833],{"fence":603,"stretchy":603,"minsize":1161,"maxsize":1161},[638,1185,642],{"mathvariant":640,"lspace":641,"rspace":641},[638,1187,842],{},[592,1189,845],{},[638,1191,827],{"stretchy":826},[592,1193,830],{},[638,1195,833],{"stretchy":826},[835,1197,837],{},[633,1199,1200,1202],{},[592,1201,991],{},[589,1203,1204,1206,1208,1210],{},[592,1205,996],{},[638,1207,827],{"stretchy":826},[592,1209,830],{},[638,1211,833],{"stretchy":826},[596,1213,1214],{"encoding":598},"\\bigl(y \\, e^{A(x)}\\bigr)' = b(x)\\,e^{A(x)}",[573,1216,1218,1327],{"className":1217,"ariaHidden":603},[602],[573,1219,1221,1225,1233,1236,1239,1281,1318,1321,1324],{"className":1220},[607],[573,1222],{"className":1223,"style":1224},[611],"height:1.3418em;vertical-align:-0.35em;",[573,1226,1228],{"className":1227},[924],[573,1229,827],{"className":1230},[1231,1232],"delimsizing","size1",[573,1234,594],{"className":1235,"style":618},[616,617],[573,1237],{"className":1238,"style":935},[902],[573,1240,1242,1245],{"className":1241},[616],[573,1243,991],{"className":1244},[616,617],[573,1246,1248],{"className":1247},[665],[573,1249,1251],{"className":1250},[669],[573,1252,1254],{"className":1253},[673],[573,1255,1258],{"className":1256,"style":1257},[677],"height:0.938em;",[573,1259,1260,1263],{"style":886},[573,1261],{"className":1262,"style":686},[685],[573,1264,1266],{"className":1265},[690,691,692,693],[573,1267,1269,1272,1275,1278],{"className":1268},[616,693],[573,1270,996],{"className":1271},[616,617,693],[573,1273,827],{"className":1274},[924,693],[573,1276,830],{"className":1277},[616,617,693],[573,1279,833],{"className":1280},[931,693],[573,1282,1284,1290],{"className":1283},[931],[573,1285,1287],{"className":1286},[931],[573,1288,833],{"className":1289},[1231,1232],[573,1291,1293],{"className":1292},[665],[573,1294,1296],{"className":1295},[669],[573,1297,1299],{"className":1298},[673],[573,1300,1303],{"className":1301,"style":1302},[677],"height:0.9918em;",[573,1304,1306,1309],{"style":1305},"top:-3.3029em;margin-right:0.05em;",[573,1307],{"className":1308,"style":686},[685],[573,1310,1312],{"className":1311},[690,691,692,693],[573,1313,1315],{"className":1314},[616,693],[573,1316,642],{"className":1317},[616,693],[573,1319],{"className":1320,"style":942},[902],[573,1322,842],{"className":1323},[946],[573,1325],{"className":1326,"style":942},[902],[573,1328,1330,1334,1337,1340,1343,1346,1349],{"className":1329},[607],[573,1331],{"className":1332,"style":1333},[611],"height:1.188em;vertical-align:-0.25em;",[573,1335,845],{"className":1336},[616,617],[573,1338,827],{"className":1339},[924],[573,1341,830],{"className":1342},[616,617],[573,1344,833],{"className":1345},[931],[573,1347],{"className":1348,"style":935},[902],[573,1350,1352,1355],{"className":1351},[616],[573,1353,991],{"className":1354},[616,617],[573,1356,1358],{"className":1357},[665],[573,1359,1361],{"className":1360},[669],[573,1362,1364],{"className":1363},[673],[573,1365,1367],{"className":1366,"style":1257},[677],[573,1368,1369,1372],{"style":886},[573,1370],{"className":1371,"style":686},[685],[573,1373,1375],{"className":1374},[690,691,692,693],[573,1376,1378,1381,1384,1387],{"className":1377},[616,693],[573,1379,996],{"className":1380},[616,617,693],[573,1382,827],{"className":1383},[924,693],[573,1385,830],{"className":1386},[616,617,693],[573,1388,833],{"className":1389},[931,693],[564,1391,1392,1393,1421,1422,1451,1452,1480,1481,1511],{},"Integrieren und Auflösen nach ",[573,1394,1396,1409],{"className":1395},[576],[573,1397,1399],{"className":1398},[580],[582,1400,1401],{"xmlns":584},[586,1402,1403,1407],{},[589,1404,1405],{},[592,1406,594],{},[596,1408,594],{"encoding":598},[573,1410,1412],{"className":1411,"ariaHidden":603},[602],[573,1413,1415,1418],{"className":1414},[607],[573,1416],{"className":1417,"style":612},[611],[573,1419,594],{"className":1420,"style":618},[616,617]," liefert die Formel. Welche Stammfunktion ",[573,1423,1425,1438],{"className":1424},[576],[573,1426,1428],{"className":1427},[580],[582,1429,1430],{"xmlns":584},[586,1431,1432,1436],{},[589,1433,1434],{},[592,1435,996],{},[596,1437,996],{"encoding":598},[573,1439,1441],{"className":1440,"ariaHidden":603},[602],[573,1442,1444,1448],{"className":1443},[607],[573,1445],{"className":1446,"style":1447},[611],"height:0.6833em;",[573,1449,996],{"className":1450},[616,617]," man nimmt, spielt keine Rolle; eine andere Konstante in ",[573,1453,1455,1468],{"className":1454},[576],[573,1456,1458],{"className":1457},[580],[582,1459,1460],{"xmlns":584},[586,1461,1462,1466],{},[589,1463,1464],{},[592,1465,996],{},[596,1467,996],{"encoding":598},[573,1469,1471],{"className":1470,"ariaHidden":603},[602],[573,1472,1474,1477],{"className":1473},[607],[573,1475],{"className":1476,"style":1447},[611],[573,1478,996],{"className":1479},[616,617]," wird von ",[573,1482,1484,1498],{"className":1483},[576],[573,1485,1487],{"className":1486},[580],[582,1488,1489],{"xmlns":584},[586,1490,1491,1496],{},[589,1492,1493],{},[592,1494,1495],{},"C",[596,1497,1495],{"encoding":598},[573,1499,1501],{"className":1500,"ariaHidden":603},[602],[573,1502,1504,1507],{"className":1503},[607],[573,1505],{"className":1506,"style":1447},[611],[573,1508,1495],{"className":1509,"style":1510},[616,617],"margin-right:0.0715em;"," aufgefangen.",[564,1513,1514,1515,1518,1519,1614,1615,1747,1748,619,1776,1805],{},"Die Lösung hat immer die Struktur ",[568,1516,1517],{},"allgemeine Lösung = homogene Lösung + eine partikuläre Lösung",". Der Teil ",[573,1520,1522,1555],{"className":1521},[576],[573,1523,1525],{"className":1524},[580],[582,1526,1527],{"xmlns":584},[586,1528,1529,1552],{},[589,1530,1531,1533,1535],{},[592,1532,1495],{},[835,1534,837],{},[633,1536,1537,1539],{},[592,1538,991],{},[589,1540,1541,1544,1546,1548,1550],{},[638,1542,1543],{},"−",[592,1545,996],{},[638,1547,827],{"stretchy":826},[592,1549,830],{},[638,1551,833],{"stretchy":826},[596,1553,1554],{"encoding":598},"C\\,e^{-A(x)}",[573,1556,1558],{"className":1557,"ariaHidden":603},[602],[573,1559,1561,1564,1567,1570],{"className":1560},[607],[573,1562],{"className":1563,"style":1015},[611],[573,1565,1495],{"className":1566,"style":1510},[616,617],[573,1568],{"className":1569,"style":935},[902],[573,1571,1573,1576],{"className":1572},[616],[573,1574,991],{"className":1575},[616,617],[573,1577,1579],{"className":1578},[665],[573,1580,1582],{"className":1581},[669],[573,1583,1585],{"className":1584},[673],[573,1586,1588],{"className":1587,"style":1015},[677],[573,1589,1590,1593],{"style":681},[573,1591],{"className":1592,"style":686},[685],[573,1594,1596],{"className":1595},[690,691,692,693],[573,1597,1599,1602,1605,1608,1611],{"className":1598},[616,693],[573,1600,1543],{"className":1601},[616,693],[573,1603,996],{"className":1604},[616,617,693],[573,1606,827],{"className":1607},[924,693],[573,1609,830],{"className":1610},[616,617,693],[573,1612,833],{"className":1613},[931,693]," löst die homogene Gleichung ",[573,1616,1618,1655],{"className":1617},[576],[573,1619,1621],{"className":1620},[580],[582,1622,1623],{"xmlns":584},[586,1624,1625,1652],{},[589,1626,1627,1633,1635,1637,1639,1641,1643,1645,1647,1649],{},[633,1628,1629,1631],{},[592,1630,594],{},[638,1632,642],{"mathvariant":640,"lspace":641,"rspace":641},[638,1634,820],{},[592,1636,823],{},[638,1638,827],{"stretchy":826},[592,1640,830],{},[638,1642,833],{"stretchy":826},[835,1644,837],{},[592,1646,594],{},[638,1648,842],{},[776,1650,1651],{},"0",[596,1653,1654],{"encoding":598},"y' + a(x)\\,y = 0",[573,1656,1658,1705,1738],{"className":1657,"ariaHidden":603},[602],[573,1659,1661,1664,1696,1699,1702],{"className":1660},[607],[573,1662],{"className":1663,"style":655},[611],[573,1665,1667,1670],{"className":1666},[616],[573,1668,594],{"className":1669,"style":618},[616,617],[573,1671,1673],{"className":1672},[665],[573,1674,1676],{"className":1675},[669],[573,1677,1679],{"className":1678},[673],[573,1680,1682],{"className":1681,"style":678},[677],[573,1683,1684,1687],{"style":681},[573,1685],{"className":1686,"style":686},[685],[573,1688,1690],{"className":1689},[690,691,692,693],[573,1691,1693],{"className":1692},[616,693],[573,1694,642],{"className":1695},[616,693],[573,1697],{"className":1698,"style":903},[902],[573,1700,820],{"className":1701},[907],[573,1703],{"className":1704,"style":903},[902],[573,1706,1708,1711,1714,1717,1720,1723,1726,1729,1732,1735],{"className":1707},[607],[573,1709],{"className":1710,"style":917},[611],[573,1712,823],{"className":1713},[616,617],[573,1715,827],{"className":1716},[924],[573,1718,830],{"className":1719},[616,617],[573,1721,833],{"className":1722},[931],[573,1724],{"className":1725,"style":935},[902],[573,1727,594],{"className":1728,"style":618},[616,617],[573,1730],{"className":1731,"style":942},[902],[573,1733,842],{"className":1734},[946],[573,1736],{"className":1737,"style":942},[902],[573,1739,1741,1744],{"className":1740},[607],[573,1742],{"className":1743,"style":790},[611],[573,1745,1651],{"className":1746},[616],", der Rest ist eine spezielle Lösung der inhomogenen Gleichung. Sind ",[573,1749,1751,1764],{"className":1750},[576],[573,1752,1754],{"className":1753},[580],[582,1755,1756],{"xmlns":584},[586,1757,1758,1762],{},[589,1759,1760],{},[592,1761,823],{},[596,1763,823],{"encoding":598},[573,1765,1767],{"className":1766,"ariaHidden":603},[602],[573,1768,1770,1773],{"className":1769},[607],[573,1771],{"className":1772,"style":1139},[611],[573,1774,823],{"className":1775},[616,617],[573,1777,1779,1792],{"className":1778},[576],[573,1780,1782],{"className":1781},[580],[582,1783,1784],{"xmlns":584},[586,1785,1786,1790],{},[589,1787,1788],{},[592,1789,845],{},[596,1791,845],{"encoding":598},[573,1793,1795],{"className":1794,"ariaHidden":603},[602],[573,1796,1798,1802],{"className":1797},[607],[573,1799],{"className":1800,"style":1801},[611],"height:0.6944em;",[573,1803,845],{"className":1804},[616,617]," auf einem Intervall stetig, gibt es zu jedem Anfangswert genau eine Lösung auf dem ganzen Intervall.",[559,1807,1809],{"id":1808},"beispiele","Beispiele",[564,1811,1812,1926,1927,1993,1994,2045,2046,2045,2117,794],{},[573,1813,1815,1845],{"className":1814},[576],[573,1816,1818],{"className":1817},[580],[582,1819,1820],{"xmlns":584},[586,1821,1822,1842],{},[589,1823,1824,1830,1832,1835,1837,1839],{},[633,1825,1826,1828],{},[592,1827,594],{},[638,1829,642],{"mathvariant":640,"lspace":641,"rspace":641},[638,1831,820],{},[776,1833,1834],{},"2",[592,1836,594],{},[638,1838,842],{},[776,1840,1841],{},"4",[596,1843,1844],{"encoding":598},"y' + 2y = 4",[573,1846,1848,1895,1917],{"className":1847,"ariaHidden":603},[602],[573,1849,1851,1854,1886,1889,1892],{"className":1850},[607],[573,1852],{"className":1853,"style":655},[611],[573,1855,1857,1860],{"className":1856},[616],[573,1858,594],{"className":1859,"style":618},[616,617],[573,1861,1863],{"className":1862},[665],[573,1864,1866],{"className":1865},[669],[573,1867,1869],{"className":1868},[673],[573,1870,1872],{"className":1871,"style":678},[677],[573,1873,1874,1877],{"style":681},[573,1875],{"className":1876,"style":686},[685],[573,1878,1880],{"className":1879},[690,691,692,693],[573,1881,1883],{"className":1882},[616,693],[573,1884,642],{"className":1885},[616,693],[573,1887],{"className":1888,"style":903},[902],[573,1890,820],{"className":1891},[907],[573,1893],{"className":1894,"style":903},[902],[573,1896,1898,1902,1905,1908,1911,1914],{"className":1897},[607],[573,1899],{"className":1900,"style":1901},[611],"height:0.8389em;vertical-align:-0.1944em;",[573,1903,1834],{"className":1904},[616],[573,1906,594],{"className":1907,"style":618},[616,617],[573,1909],{"className":1910,"style":942},[902],[573,1912,842],{"className":1913},[946],[573,1915],{"className":1916,"style":942},[902],[573,1918,1920,1923],{"className":1919},[607],[573,1921],{"className":1922,"style":790},[611],[573,1924,1841],{"className":1925},[616]," mit ",[573,1928,1930,1954],{"className":1929},[576],[573,1931,1933],{"className":1932},[580],[582,1934,1935],{"xmlns":584},[586,1936,1937,1951],{},[589,1938,1939,1941,1943,1945,1947,1949],{},[592,1940,594],{},[638,1942,827],{"stretchy":826},[776,1944,1651],{},[638,1946,833],{"stretchy":826},[638,1948,842],{},[776,1950,1651],{},[596,1952,1953],{"encoding":598},"y(0) = 0",[573,1955,1957,1984],{"className":1956,"ariaHidden":603},[602],[573,1958,1960,1963,1966,1969,1972,1975,1978,1981],{"className":1959},[607],[573,1961],{"className":1962,"style":917},[611],[573,1964,594],{"className":1965,"style":618},[616,617],[573,1967,827],{"className":1968},[924],[573,1970,1651],{"className":1971},[616],[573,1973,833],{"className":1974},[931],[573,1976],{"className":1977,"style":942},[902],[573,1979,842],{"className":1980},[946],[573,1982],{"className":1983,"style":942},[902],[573,1985,1987,1990],{"className":1986},[607],[573,1988],{"className":1989,"style":790},[611],[573,1991,1651],{"className":1992},[616],". Hier ist ",[573,1995,1997,2015],{"className":1996},[576],[573,1998,2000],{"className":1999},[580],[582,2001,2002],{"xmlns":584},[586,2003,2004,2012],{},[589,2005,2006,2008,2010],{},[592,2007,823],{},[638,2009,842],{},[776,2011,1834],{},[596,2013,2014],{"encoding":598},"a = 2",[573,2016,2018,2036],{"className":2017,"ariaHidden":603},[602],[573,2019,2021,2024,2027,2030,2033],{"className":2020},[607],[573,2022],{"className":2023,"style":1139},[611],[573,2025,823],{"className":2026},[616,617],[573,2028],{"className":2029,"style":942},[902],[573,2031,842],{"className":2032},[946],[573,2034],{"className":2035,"style":942},[902],[573,2037,2039,2042],{"className":2038},[607],[573,2040],{"className":2041,"style":790},[611],[573,2043,1834],{"className":2044},[616],", ",[573,2047,2049,2075],{"className":2048},[576],[573,2050,2052],{"className":2051},[580],[582,2053,2054],{"xmlns":584},[586,2055,2056,2072],{},[589,2057,2058,2060,2062,2064,2066,2068,2070],{},[592,2059,996],{},[638,2061,827],{"stretchy":826},[592,2063,830],{},[638,2065,833],{"stretchy":826},[638,2067,842],{},[776,2069,1834],{},[592,2071,830],{},[596,2073,2074],{"encoding":598},"A(x) = 2x",[573,2076,2078,2105],{"className":2077,"ariaHidden":603},[602],[573,2079,2081,2084,2087,2090,2093,2096,2099,2102],{"className":2080},[607],[573,2082],{"className":2083,"style":917},[611],[573,2085,996],{"className":2086},[616,617],[573,2088,827],{"className":2089},[924],[573,2091,830],{"className":2092},[616,617],[573,2094,833],{"className":2095},[931],[573,2097],{"className":2098,"style":942},[902],[573,2100,842],{"className":2101},[946],[573,2103],{"className":2104,"style":942},[902],[573,2106,2108,2111,2114],{"className":2107},[607],[573,2109],{"className":2110,"style":790},[611],[573,2112,1834],{"className":2113},[616],[573,2115,830],{"className":2116},[616,617],[573,2118,2120,2138],{"className":2119},[576],[573,2121,2123],{"className":2122},[580],[582,2124,2125],{"xmlns":584},[586,2126,2127,2135],{},[589,2128,2129,2131,2133],{},[592,2130,845],{},[638,2132,842],{},[776,2134,1841],{},[596,2136,2137],{"encoding":598},"b = 4",[573,2139,2141,2159],{"className":2140,"ariaHidden":603},[602],[573,2142,2144,2147,2150,2153,2156],{"className":2143},[607],[573,2145],{"className":2146,"style":1801},[611],[573,2148,845],{"className":2149},[616,617],[573,2151],{"className":2152,"style":942},[902],[573,2154,842],{"className":2155},[946],[573,2157],{"className":2158,"style":942},[902],[573,2160,2162,2165],{"className":2161},[607],[573,2163],{"className":2164,"style":790},[611],[573,2166,1841],{"className":2167},[616],[573,2169,2171],{"className":2170},[798],[573,2172,2174,2296],{"className":2173},[576],[573,2175,2177],{"className":2176},[580],[582,2178,2179],{"xmlns":584,"display":807},[586,2180,2181,2293],{},[589,2182,2183,2185,2187,2199,2233,2235,2247,2271,2273,2275,2277,2279,2281],{},[592,2184,594],{},[638,2186,842],{},[633,2188,2189,2191],{},[592,2190,991],{},[589,2192,2193,2195,2197],{},[638,2194,1543],{},[776,2196,1834],{},[592,2198,830],{},[589,2200,2201,2203,2206,2208,2210,2220,2222,2225,2227,2229,2231],{},[638,2202,827],{"fence":603},[638,2204,2205],{},"∫",[776,2207,1841],{},[835,2209,837],{},[633,2211,2212,2214],{},[592,2213,991],{},[589,2215,2216,2218],{},[776,2217,1834],{},[592,2219,830],{},[835,2221,837],{},[592,2223,2224],{},"d",[592,2226,830],{},[638,2228,820],{},[592,2230,1495],{},[638,2232,833],{"fence":603},[638,2234,842],{},[633,2236,2237,2239],{},[592,2238,991],{},[589,2240,2241,2243,2245],{},[638,2242,1543],{},[776,2244,1834],{},[592,2246,830],{},[589,2248,2249,2251,2253,2255,2265,2267,2269],{},[638,2250,827],{"fence":603},[776,2252,1834],{},[835,2254,837],{},[633,2256,2257,2259],{},[592,2258,991],{},[589,2260,2261,2263],{},[776,2262,1834],{},[592,2264,830],{},[638,2266,820],{},[592,2268,1495],{},[638,2270,833],{"fence":603},[638,2272,842],{},[776,2274,1834],{},[638,2276,820],{},[592,2278,1495],{},[835,2280,837],{},[633,2282,2283,2285],{},[592,2284,991],{},[589,2286,2287,2289,2291],{},[638,2288,1543],{},[776,2290,1834],{},[592,2292,830],{},[596,2294,2295],{"encoding":598},"y = e^{-2x} \\left( \\int 4\\,e^{2x}\\,dx + C \\right) = e^{-2x} \\left( 2\\,e^{2x} + C \\right) = 2 + C\\,e^{-2x}",[573,2297,2299,2317,2465,2590,2609],{"className":2298,"ariaHidden":603},[602],[573,2300,2302,2305,2308,2311,2314],{"className":2301},[607],[573,2303],{"className":2304,"style":612},[611],[573,2306,594],{"className":2307,"style":618},[616,617],[573,2309],{"className":2310,"style":942},[902],[573,2312,842],{"className":2313},[946],[573,2315],{"className":2316,"style":942},[902],[573,2318,2320,2324,2363,2366,2456,2459,2462],{"className":2319},[607],[573,2321],{"className":2322,"style":2323},[611],"height:2.4em;vertical-align:-0.95em;",[573,2325,2327,2330],{"className":2326},[616],[573,2328,991],{"className":2329},[616,617],[573,2331,2333],{"className":2332},[665],[573,2334,2336],{"className":2335},[669],[573,2337,2339],{"className":2338},[673],[573,2340,2343],{"className":2341,"style":2342},[677],"height:0.8641em;",[573,2344,2345,2348],{"style":886},[573,2346],{"className":2347,"style":686},[685],[573,2349,2351],{"className":2350},[690,691,692,693],[573,2352,2354,2357,2360],{"className":2353},[616,693],[573,2355,1543],{"className":2356},[616,693],[573,2358,1834],{"className":2359},[616,693],[573,2361,830],{"className":2362},[616,617,693],[573,2364],{"className":2365,"style":935},[902],[573,2367,2370,2378,2385,2388,2391,2394,2429,2432,2435,2438,2441,2444,2447,2450],{"className":2368},[2369],"minner",[573,2371,2375],{"className":2372,"style":2374},[924,2373],"delimcenter","top:0em;",[573,2376,827],{"className":2377},[1231,692],[573,2379,2205],{"className":2380,"style":2384},[2381,2382,2383],"mop","op-symbol","large-op","margin-right:0.4445em;position:relative;top:-0.0011em;",[573,2386],{"className":2387,"style":935},[902],[573,2389,1841],{"className":2390},[616],[573,2392],{"className":2393,"style":935},[902],[573,2395,2397,2400],{"className":2396},[616],[573,2398,991],{"className":2399},[616,617],[573,2401,2403],{"className":2402},[665],[573,2404,2406],{"className":2405},[669],[573,2407,2409],{"className":2408},[673],[573,2410,2412],{"className":2411,"style":2342},[677],[573,2413,2414,2417],{"style":886},[573,2415],{"className":2416,"style":686},[685],[573,2418,2420],{"className":2419},[690,691,692,693],[573,2421,2423,2426],{"className":2422},[616,693],[573,2424,1834],{"className":2425},[616,693],[573,2427,830],{"className":2428},[616,617,693],[573,2430],{"className":2431,"style":935},[902],[573,2433,2224],{"className":2434},[616,617],[573,2436,830],{"className":2437},[616,617],[573,2439],{"className":2440,"style":903},[902],[573,2442,820],{"className":2443},[907],[573,2445],{"className":2446,"style":903},[902],[573,2448,1495],{"className":2449,"style":1510},[616,617],[573,2451,2453],{"className":2452,"style":2374},[931,2373],[573,2454,833],{"className":2455},[1231,692],[573,2457],{"className":2458,"style":942},[902],[573,2460,842],{"className":2461},[946],[573,2463],{"className":2464,"style":942},[902],[573,2466,2468,2472,2510,2513,2581,2584,2587],{"className":2467},[607],[573,2469],{"className":2470,"style":2471},[611],"height:1.2141em;vertical-align:-0.35em;",[573,2473,2475,2478],{"className":2474},[616],[573,2476,991],{"className":2477},[616,617],[573,2479,2481],{"className":2480},[665],[573,2482,2484],{"className":2483},[669],[573,2485,2487],{"className":2486},[673],[573,2488,2490],{"className":2489,"style":2342},[677],[573,2491,2492,2495],{"style":886},[573,2493],{"className":2494,"style":686},[685],[573,2496,2498],{"className":2497},[690,691,692,693],[573,2499,2501,2504,2507],{"className":2500},[616,693],[573,2502,1543],{"className":2503},[616,693],[573,2505,1834],{"className":2506},[616,693],[573,2508,830],{"className":2509},[616,617,693],[573,2511],{"className":2512,"style":935},[902],[573,2514,2516,2522,2525,2528,2563,2566,2569,2572,2575],{"className":2515},[2369],[573,2517,2519],{"className":2518,"style":2374},[924,2373],[573,2520,827],{"className":2521},[1231,1232],[573,2523,1834],{"className":2524},[616],[573,2526],{"className":2527,"style":935},[902],[573,2529,2531,2534],{"className":2530},[616],[573,2532,991],{"className":2533},[616,617],[573,2535,2537],{"className":2536},[665],[573,2538,2540],{"className":2539},[669],[573,2541,2543],{"className":2542},[673],[573,2544,2546],{"className":2545,"style":2342},[677],[573,2547,2548,2551],{"style":886},[573,2549],{"className":2550,"style":686},[685],[573,2552,2554],{"className":2553},[690,691,692,693],[573,2555,2557,2560],{"className":2556},[616,693],[573,2558,1834],{"className":2559},[616,693],[573,2561,830],{"className":2562},[616,617,693],[573,2564],{"className":2565,"style":903},[902],[573,2567,820],{"className":2568},[907],[573,2570],{"className":2571,"style":903},[902],[573,2573,1495],{"className":2574,"style":1510},[616,617],[573,2576,2578],{"className":2577,"style":2374},[931,2373],[573,2579,833],{"className":2580},[1231,1232],[573,2582],{"className":2583,"style":942},[902],[573,2585,842],{"className":2586},[946],[573,2588],{"className":2589,"style":942},[902],[573,2591,2593,2597,2600,2603,2606],{"className":2592},[607],[573,2594],{"className":2595,"style":2596},[611],"height:0.7278em;vertical-align:-0.0833em;",[573,2598,1834],{"className":2599},[616],[573,2601],{"className":2602,"style":903},[902],[573,2604,820],{"className":2605},[907],[573,2607],{"className":2608,"style":903},[902],[573,2610,2612,2615,2618,2621],{"className":2611},[607],[573,2613],{"className":2614,"style":2342},[611],[573,2616,1495],{"className":2617,"style":1510},[616,617],[573,2619],{"className":2620,"style":935},[902],[573,2622,2624,2627],{"className":2623},[616],[573,2625,991],{"className":2626},[616,617],[573,2628,2630],{"className":2629},[665],[573,2631,2633],{"className":2632},[669],[573,2634,2636],{"className":2635},[673],[573,2637,2639],{"className":2638,"style":2342},[677],[573,2640,2641,2644],{"style":886},[573,2642],{"className":2643,"style":686},[685],[573,2645,2647],{"className":2646},[690,691,692,693],[573,2648,2650,2653,2656],{"className":2649},[616,693],[573,2651,1543],{"className":2652},[616,693],[573,2654,1834],{"className":2655},[616,693],[573,2657,830],{"className":2658},[616,617,693],[564,2660,2661,2662,2772,2773,2829,2830,2959,2960,3248,3249,3423,3424,3477,3478,3506,3507,3535],{},"Aus ",[573,2663,2665,2697],{"className":2664},[576],[573,2666,2668],{"className":2667},[580],[582,2669,2670],{"xmlns":584},[586,2671,2672,2694],{},[589,2673,2674,2676,2678,2680,2682,2684,2686,2688,2690,2692],{},[592,2675,594],{},[638,2677,827],{"stretchy":826},[776,2679,1651],{},[638,2681,833],{"stretchy":826},[638,2683,842],{},[776,2685,1834],{},[638,2687,820],{},[592,2689,1495],{},[638,2691,842],{},[776,2693,1651],{},[596,2695,2696],{"encoding":598},"y(0) = 2 + C = 0",[573,2698,2700,2727,2745,2763],{"className":2699,"ariaHidden":603},[602],[573,2701,2703,2706,2709,2712,2715,2718,2721,2724],{"className":2702},[607],[573,2704],{"className":2705,"style":917},[611],[573,2707,594],{"className":2708,"style":618},[616,617],[573,2710,827],{"className":2711},[924],[573,2713,1651],{"className":2714},[616],[573,2716,833],{"className":2717},[931],[573,2719],{"className":2720,"style":942},[902],[573,2722,842],{"className":2723},[946],[573,2725],{"className":2726,"style":942},[902],[573,2728,2730,2733,2736,2739,2742],{"className":2729},[607],[573,2731],{"className":2732,"style":2596},[611],[573,2734,1834],{"className":2735},[616],[573,2737],{"className":2738,"style":903},[902],[573,2740,820],{"className":2741},[907],[573,2743],{"className":2744,"style":903},[902],[573,2746,2748,2751,2754,2757,2760],{"className":2747},[607],[573,2749],{"className":2750,"style":1447},[611],[573,2752,1495],{"className":2753,"style":1510},[616,617],[573,2755],{"className":2756,"style":942},[902],[573,2758,842],{"className":2759},[946],[573,2761],{"className":2762,"style":942},[902],[573,2764,2766,2769],{"className":2765},[607],[573,2767],{"className":2768,"style":790},[611],[573,2770,1651],{"className":2771},[616]," folgt ",[573,2774,2776,2796],{"className":2775},[576],[573,2777,2779],{"className":2778},[580],[582,2780,2781],{"xmlns":584},[586,2782,2783,2793],{},[589,2784,2785,2787,2789,2791],{},[592,2786,1495],{},[638,2788,842],{},[638,2790,1543],{},[776,2792,1834],{},[596,2794,2795],{"encoding":598},"C = -2",[573,2797,2799,2817],{"className":2798,"ariaHidden":603},[602],[573,2800,2802,2805,2808,2811,2814],{"className":2801},[607],[573,2803],{"className":2804,"style":1447},[611],[573,2806,1495],{"className":2807,"style":1510},[616,617],[573,2809],{"className":2810,"style":942},[902],[573,2812,842],{"className":2813},[946],[573,2815],{"className":2816,"style":942},[902],[573,2818,2820,2823,2826],{"className":2819},[607],[573,2821],{"className":2822,"style":2596},[611],[573,2824,1543],{"className":2825},[616],[573,2827,1834],{"className":2828},[616],", also ",[573,2831,2833,2869],{"className":2832},[576],[573,2834,2836],{"className":2835},[580],[582,2837,2838],{"xmlns":584},[586,2839,2840,2866],{},[589,2841,2842,2844,2846,2848,2850,2852,2854],{},[592,2843,594],{},[638,2845,842],{},[776,2847,1834],{},[638,2849,1543],{},[776,2851,1834],{},[835,2853,837],{},[633,2855,2856,2858],{},[592,2857,991],{},[589,2859,2860,2862,2864],{},[638,2861,1543],{},[776,2863,1834],{},[592,2865,830],{},[596,2867,2868],{"encoding":598},"y = 2 - 2\\,e^{-2x}",[573,2870,2872,2890,2908],{"className":2871,"ariaHidden":603},[602],[573,2873,2875,2878,2881,2884,2887],{"className":2874},[607],[573,2876],{"className":2877,"style":612},[611],[573,2879,594],{"className":2880,"style":618},[616,617],[573,2882],{"className":2883,"style":942},[902],[573,2885,842],{"className":2886},[946],[573,2888],{"className":2889,"style":942},[902],[573,2891,2893,2896,2899,2902,2905],{"className":2892},[607],[573,2894],{"className":2895,"style":2596},[611],[573,2897,1834],{"className":2898},[616],[573,2900],{"className":2901,"style":903},[902],[573,2903,1543],{"className":2904},[907],[573,2906],{"className":2907,"style":903},[902],[573,2909,2911,2915,2918,2921],{"className":2910},[607],[573,2912],{"className":2913,"style":2914},[611],"height:0.8141em;",[573,2916,1834],{"className":2917},[616],[573,2919],{"className":2920,"style":935},[902],[573,2922,2924,2927],{"className":2923},[616],[573,2925,991],{"className":2926},[616,617],[573,2928,2930],{"className":2929},[665],[573,2931,2933],{"className":2932},[669],[573,2934,2936],{"className":2935},[673],[573,2937,2939],{"className":2938,"style":2914},[677],[573,2940,2941,2944],{"style":681},[573,2942],{"className":2943,"style":686},[685],[573,2945,2947],{"className":2946},[690,691,692,693],[573,2948,2950,2953,2956],{"className":2949},[616,693],[573,2951,1543],{"className":2952},[616,693],[573,2954,1834],{"className":2955},[616,693],[573,2957,830],{"className":2958},[616,617,693],". Probe: ",[573,2961,2963,3031],{"className":2962},[576],[573,2964,2966],{"className":2965},[580],[582,2967,2968],{"xmlns":584},[586,2969,2970,3028],{},[589,2971,2972,2978,2980,2982,2984,2986,2988,2990,3002,3004,3006,3008,3010,3012,3024,3026],{},[633,2973,2974,2976],{},[592,2975,594],{},[638,2977,642],{"mathvariant":640,"lspace":641,"rspace":641},[638,2979,820],{},[776,2981,1834],{},[592,2983,594],{},[638,2985,842],{},[776,2987,1841],{},[835,2989,837],{},[633,2991,2992,2994],{},[592,2993,991],{},[589,2995,2996,2998,3000],{},[638,2997,1543],{},[776,2999,1834],{},[592,3001,830],{},[638,3003,820],{},[776,3005,1841],{},[638,3007,1543],{},[776,3009,1841],{},[835,3011,837],{},[633,3013,3014,3016],{},[592,3015,991],{},[589,3017,3018,3020,3022],{},[638,3019,1543],{},[776,3021,1834],{},[592,3023,830],{},[638,3025,842],{},[776,3027,1841],{},[596,3029,3030],{"encoding":598},"y' + 2y = 4\\,e^{-2x} + 4 - 4\\,e^{-2x} = 4",[573,3032,3034,3081,3102,3162,3180,3239],{"className":3033,"ariaHidden":603},[602],[573,3035,3037,3040,3072,3075,3078],{"className":3036},[607],[573,3038],{"className":3039,"style":655},[611],[573,3041,3043,3046],{"className":3042},[616],[573,3044,594],{"className":3045,"style":618},[616,617],[573,3047,3049],{"className":3048},[665],[573,3050,3052],{"className":3051},[669],[573,3053,3055],{"className":3054},[673],[573,3056,3058],{"className":3057,"style":678},[677],[573,3059,3060,3063],{"style":681},[573,3061],{"className":3062,"style":686},[685],[573,3064,3066],{"className":3065},[690,691,692,693],[573,3067,3069],{"className":3068},[616,693],[573,3070,642],{"className":3071},[616,693],[573,3073],{"className":3074,"style":903},[902],[573,3076,820],{"className":3077},[907],[573,3079],{"className":3080,"style":903},[902],[573,3082,3084,3087,3090,3093,3096,3099],{"className":3083},[607],[573,3085],{"className":3086,"style":1901},[611],[573,3088,1834],{"className":3089},[616],[573,3091,594],{"className":3092,"style":618},[616,617],[573,3094],{"className":3095,"style":942},[902],[573,3097,842],{"className":3098},[946],[573,3100],{"className":3101,"style":942},[902],[573,3103,3105,3109,3112,3115,3153,3156,3159],{"className":3104},[607],[573,3106],{"className":3107,"style":3108},[611],"height:0.8974em;vertical-align:-0.0833em;",[573,3110,1841],{"className":3111},[616],[573,3113],{"className":3114,"style":935},[902],[573,3116,3118,3121],{"className":3117},[616],[573,3119,991],{"className":3120},[616,617],[573,3122,3124],{"className":3123},[665],[573,3125,3127],{"className":3126},[669],[573,3128,3130],{"className":3129},[673],[573,3131,3133],{"className":3132,"style":2914},[677],[573,3134,3135,3138],{"style":681},[573,3136],{"className":3137,"style":686},[685],[573,3139,3141],{"className":3140},[690,691,692,693],[573,3142,3144,3147,3150],{"className":3143},[616,693],[573,3145,1543],{"className":3146},[616,693],[573,3148,1834],{"className":3149},[616,693],[573,3151,830],{"className":3152},[616,617,693],[573,3154],{"className":3155,"style":903},[902],[573,3157,820],{"className":3158},[907],[573,3160],{"className":3161,"style":903},[902],[573,3163,3165,3168,3171,3174,3177],{"className":3164},[607],[573,3166],{"className":3167,"style":2596},[611],[573,3169,1841],{"className":3170},[616],[573,3172],{"className":3173,"style":903},[902],[573,3175,1543],{"className":3176},[907],[573,3178],{"className":3179,"style":903},[902],[573,3181,3183,3186,3189,3192,3230,3233,3236],{"className":3182},[607],[573,3184],{"className":3185,"style":2914},[611],[573,3187,1841],{"className":3188},[616],[573,3190],{"className":3191,"style":935},[902],[573,3193,3195,3198],{"className":3194},[616],[573,3196,991],{"className":3197},[616,617],[573,3199,3201],{"className":3200},[665],[573,3202,3204],{"className":3203},[669],[573,3205,3207],{"className":3206},[673],[573,3208,3210],{"className":3209,"style":2914},[677],[573,3211,3212,3215],{"style":681},[573,3213],{"className":3214,"style":686},[685],[573,3216,3218],{"className":3217},[690,691,692,693],[573,3219,3221,3224,3227],{"className":3220},[616,693],[573,3222,1543],{"className":3223},[616,693],[573,3225,1834],{"className":3226},[616,693],[573,3228,830],{"className":3229},[616,617,693],[573,3231],{"className":3232,"style":942},[902],[573,3234,842],{"className":3235},[946],[573,3237],{"className":3238,"style":942},[902],[573,3240,3242,3245],{"className":3241},[607],[573,3243],{"className":3244,"style":790},[611],[573,3246,1841],{"className":3247},[616],". Es ist ",[573,3250,3252,3298],{"className":3251},[576],[573,3253,3255],{"className":3254},[580],[582,3256,3257],{"xmlns":584},[586,3258,3259,3295],{},[589,3260,3261,3263,3265,3267,3269,3271,3273,3275,3277,3279,3289,3292],{},[592,3262,594],{},[638,3264,827],{"stretchy":826},[776,3266,778],{},[638,3268,833],{"stretchy":826},[638,3270,842],{},[776,3272,1834],{},[638,3274,1543],{},[776,3276,1834],{},[835,3278,837],{},[633,3280,3281,3283],{},[592,3282,991],{},[589,3284,3285,3287],{},[638,3286,1543],{},[776,3288,1834],{},[638,3290,3291],{},"≈",[776,3293,3294],{},"1,7293",[596,3296,3297],{"encoding":598},"y(1) = 2 - 2\\,e^{-2} \\approx 1{,}7293",[573,3299,3301,3328,3346,3402],{"className":3300,"ariaHidden":603},[602],[573,3302,3304,3307,3310,3313,3316,3319,3322,3325],{"className":3303},[607],[573,3305],{"className":3306,"style":917},[611],[573,3308,594],{"className":3309,"style":618},[616,617],[573,3311,827],{"className":3312},[924],[573,3314,778],{"className":3315},[616],[573,3317,833],{"className":3318},[931],[573,3320],{"className":3321,"style":942},[902],[573,3323,842],{"className":3324},[946],[573,3326],{"className":3327,"style":942},[902],[573,3329,3331,3334,3337,3340,3343],{"className":3330},[607],[573,3332],{"className":3333,"style":2596},[611],[573,3335,1834],{"className":3336},[616],[573,3338],{"className":3339,"style":903},[902],[573,3341,1543],{"className":3342},[907],[573,3344],{"className":3345,"style":903},[902],[573,3347,3349,3352,3355,3358,3393,3396,3399],{"className":3348},[607],[573,3350],{"className":3351,"style":2914},[611],[573,3353,1834],{"className":3354},[616],[573,3356],{"className":3357,"style":935},[902],[573,3359,3361,3364],{"className":3360},[616],[573,3362,991],{"className":3363},[616,617],[573,3365,3367],{"className":3366},[665],[573,3368,3370],{"className":3369},[669],[573,3371,3373],{"className":3372},[673],[573,3374,3376],{"className":3375,"style":2914},[677],[573,3377,3378,3381],{"style":681},[573,3379],{"className":3380,"style":686},[685],[573,3382,3384],{"className":3383},[690,691,692,693],[573,3385,3387,3390],{"className":3386},[616,693],[573,3388,1543],{"className":3389},[616,693],[573,3391,1834],{"className":3392},[616,693],[573,3394],{"className":3395,"style":942},[902],[573,3397,3291],{"className":3398},[946],[573,3400],{"className":3401,"style":942},[902],[573,3403,3405,3408,3411,3419],{"className":3404},[607],[573,3406],{"className":3407,"style":1901},[611],[573,3409,778],{"className":3410},[616],[573,3412,3414],{"className":3413},[616],[573,3415,3418],{"className":3416},[3417],"mpunct",",",[573,3420,3422],{"className":3421},[616],"7293","; für ",[573,3425,3427,3447],{"className":3426},[576],[573,3428,3430],{"className":3429},[580],[582,3431,3432],{"xmlns":584},[586,3433,3434,3444],{},[589,3435,3436,3438,3441],{},[592,3437,830],{},[638,3439,3440],{},"→",[592,3442,3443],{"mathvariant":640},"∞",[596,3445,3446],{"encoding":598},"x \\to \\infty",[573,3448,3450,3468],{"className":3449,"ariaHidden":603},[602],[573,3451,3453,3456,3459,3462,3465],{"className":3452},[607],[573,3454],{"className":3455,"style":1139},[611],[573,3457,830],{"className":3458},[616,617],[573,3460],{"className":3461,"style":942},[902],[573,3463,3440],{"className":3464},[946],[573,3466],{"className":3467,"style":942},[902],[573,3469,3471,3474],{"className":3470},[607],[573,3472],{"className":3473,"style":1139},[611],[573,3475,3443],{"className":3476},[616]," nähert sich ",[573,3479,3481,3494],{"className":3480},[576],[573,3482,3484],{"className":3483},[580],[582,3485,3486],{"xmlns":584},[586,3487,3488,3492],{},[589,3489,3490],{},[592,3491,594],{},[596,3493,594],{"encoding":598},[573,3495,3497],{"className":3496,"ariaHidden":603},[602],[573,3498,3500,3503],{"className":3499},[607],[573,3501],{"className":3502,"style":612},[611],[573,3504,594],{"className":3505,"style":618},[616,617]," dem Wert ",[573,3508,3510,3523],{"className":3509},[576],[573,3511,3513],{"className":3512},[580],[582,3514,3515],{"xmlns":584},[586,3516,3517,3521],{},[589,3518,3519],{},[776,3520,1834],{},[596,3522,1834],{"encoding":598},[573,3524,3526],{"className":3525,"ariaHidden":603},[602],[573,3527,3529,3532],{"className":3528},[607],[573,3530],{"className":3531,"style":790},[611],[573,3533,1834],{"className":3534},[616],".",[564,3537,3538,3737,3738,3791,3792,3870,3871,794],{},[573,3539,3541,3576],{"className":3540},[576],[573,3542,3544],{"className":3543},[580],[582,3545,3546],{"xmlns":584},[586,3547,3548,3573],{},[589,3549,3550,3556,3558,3565,3567,3569,3571],{},[633,3551,3552,3554],{},[592,3553,594],{},[638,3555,642],{"mathvariant":640,"lspace":641,"rspace":641},[638,3557,820],{},[3559,3560,3561,3563],"mfrac",{},[776,3562,778],{},[592,3564,830],{},[835,3566,837],{},[592,3568,594],{},[638,3570,842],{},[592,3572,830],{},[596,3574,3575],{"encoding":598},"y' + \\frac{1}{x}\\,y = x",[573,3577,3579,3626,3728],{"className":3578,"ariaHidden":603},[602],[573,3580,3582,3585,3617,3620,3623],{"className":3581},[607],[573,3583],{"className":3584,"style":655},[611],[573,3586,3588,3591],{"className":3587},[616],[573,3589,594],{"className":3590,"style":618},[616,617],[573,3592,3594],{"className":3593},[665],[573,3595,3597],{"className":3596},[669],[573,3598,3600],{"className":3599},[673],[573,3601,3603],{"className":3602,"style":678},[677],[573,3604,3605,3608],{"style":681},[573,3606],{"className":3607,"style":686},[685],[573,3609,3611],{"className":3610},[690,691,692,693],[573,3612,3614],{"className":3613},[616,693],[573,3615,642],{"className":3616},[616,693],[573,3618],{"className":3619,"style":903},[902],[573,3621,820],{"className":3622},[907],[573,3624],{"className":3625,"style":903},[902],[573,3627,3629,3633,3713,3716,3719,3722,3725],{"className":3628},[607],[573,3630],{"className":3631,"style":3632},[611],"height:1.1901em;vertical-align:-0.345em;",[573,3634,3636,3640,3710],{"className":3635},[616],[573,3637],{"className":3638},[924,3639],"nulldelimiter",[573,3641,3643],{"className":3642},[3559],[573,3644,3647,3701],{"className":3645},[669,3646],"vlist-t2",[573,3648,3650,3696],{"className":3649},[673],[573,3651,3654,3670,3681],{"className":3652,"style":3653},[677],"height:0.8451em;",[573,3655,3657,3661],{"style":3656},"top:-2.655em;",[573,3658],{"className":3659,"style":3660},[685],"height:3em;",[573,3662,3664],{"className":3663},[690,691,692,693],[573,3665,3667],{"className":3666},[616,693],[573,3668,830],{"className":3669},[616,617,693],[573,3671,3673,3676],{"style":3672},"top:-3.23em;",[573,3674],{"className":3675,"style":3660},[685],[573,3677],{"className":3678,"style":3680},[3679],"frac-line","border-bottom-width:0.04em;",[573,3682,3684,3687],{"style":3683},"top:-3.394em;",[573,3685],{"className":3686,"style":3660},[685],[573,3688,3690],{"className":3689},[690,691,692,693],[573,3691,3693],{"className":3692},[616,693],[573,3694,778],{"className":3695},[616,693],[573,3697,3700],{"className":3698},[3699],"vlist-s","​",[573,3702,3704],{"className":3703},[673],[573,3705,3708],{"className":3706,"style":3707},[677],"height:0.345em;",[573,3709],{},[573,3711],{"className":3712},[931,3639],[573,3714],{"className":3715,"style":935},[902],[573,3717,594],{"className":3718,"style":618},[616,617],[573,3720],{"className":3721,"style":942},[902],[573,3723,842],{"className":3724},[946],[573,3726],{"className":3727,"style":942},[902],[573,3729,3731,3734],{"className":3730},[607],[573,3732],{"className":3733,"style":1139},[611],[573,3735,830],{"className":3736},[616,617]," für ",[573,3739,3741,3760],{"className":3740},[576],[573,3742,3744],{"className":3743},[580],[582,3745,3746],{"xmlns":584},[586,3747,3748,3757],{},[589,3749,3750,3752,3755],{},[592,3751,830],{},[638,3753,3754],{},">",[776,3756,1651],{},[596,3758,3759],{"encoding":598},"x > 0",[573,3761,3763,3782],{"className":3762,"ariaHidden":603},[602],[573,3764,3766,3770,3773,3776,3779],{"className":3765},[607],[573,3767],{"className":3768,"style":3769},[611],"height:0.5782em;vertical-align:-0.0391em;",[573,3771,830],{"className":3772},[616,617],[573,3774],{"className":3775,"style":942},[902],[573,3777,3754],{"className":3778},[946],[573,3780],{"className":3781,"style":942},[902],[573,3783,3785,3788],{"className":3784},[607],[573,3786],{"className":3787,"style":790},[611],[573,3789,1651],{"className":3790},[616],". Mit ",[573,3793,3795,3825],{"className":3794},[576],[573,3796,3798],{"className":3797},[580],[582,3799,3800],{"xmlns":584},[586,3801,3802,3822],{},[589,3803,3804,3806,3808,3810,3812,3814,3817,3820],{},[592,3805,996],{},[638,3807,827],{"stretchy":826},[592,3809,830],{},[638,3811,833],{"stretchy":826},[638,3813,842],{},[592,3815,3816],{},"ln",[638,3818,3819],{},"⁡",[592,3821,830],{},[596,3823,3824],{"encoding":598},"A(x) = \\ln x",[573,3826,3828,3855],{"className":3827,"ariaHidden":603},[602],[573,3829,3831,3834,3837,3840,3843,3846,3849,3852],{"className":3830},[607],[573,3832],{"className":3833,"style":917},[611],[573,3835,996],{"className":3836},[616,617],[573,3838,827],{"className":3839},[924],[573,3841,830],{"className":3842},[616,617],[573,3844,833],{"className":3845},[931],[573,3847],{"className":3848,"style":942},[902],[573,3850,842],{"className":3851},[946],[573,3853],{"className":3854,"style":942},[902],[573,3856,3858,3861,3864,3867],{"className":3857},[607],[573,3859],{"className":3860,"style":1801},[611],[573,3862,3816],{"className":3863},[2381],[573,3865],{"className":3866,"style":935},[902],[573,3868,830],{"className":3869},[616,617]," ist ",[573,3872,3874,3904],{"className":3873},[576],[573,3875,3877],{"className":3876},[580],[582,3878,3879],{"xmlns":584},[586,3880,3881,3901],{},[589,3882,3883,3897,3899],{},[633,3884,3885,3887],{},[592,3886,991],{},[589,3888,3889,3891,3893,3895],{},[592,3890,996],{},[638,3892,827],{"stretchy":826},[592,3894,830],{},[638,3896,833],{"stretchy":826},[638,3898,842],{},[592,3900,830],{},[596,3902,3903],{"encoding":598},"e^{A(x)} = 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im Integral ",[573,4964,4966,4988],{"className":4965},[576],[573,4967,4969],{"className":4968},[580],[582,4970,4971],{"xmlns":584},[586,4972,4973,4985],{},[589,4974,4975],{},[633,4976,4977,4979],{},[592,4978,991],{},[589,4980,4981,4983],{},[638,4982,820],{},[592,4984,996],{},[596,4986,4987],{"encoding":598},"e^{+A}",[573,4989,4991],{"className":4990,"ariaHidden":603},[602],[573,4992,4994,4997],{"className":4993},[607],[573,4995],{"className":4996,"style":4926},[611],[573,4998,5000,5003],{"className":4999},[616],[573,5001,991],{"className":5002},[616,617],[573,5004,5006],{"className":5005},[665],[573,5007,5009],{"className":5008},[669],[573,5010,5012],{"className":5011},[673],[573,5013,5015],{"className":5014,"style":4926},[677],[573,5016,5017,5020],{"style":681},[573,5018],{"className":5019,"style":686},[685],[573,5021,5023],{"className":5022},[690,691,692,693],[573,5024,5026,5029],{"className":5025},[616,693],[573,5027,820],{"className":5028},[616,693],[573,5030,996],{"className":5031},[616,617,693],[4615,5033,5034,5035,5225,5226,3535],{},"Die Konstante außerhalb der Klammer addieren: ",[573,5036,5038,5086],{"className":5037},[576],[573,5039,5041],{"className":5040},[580],[582,5042,5043],{"xmlns":584},[586,5044,5045,5083],{},[589,5046,5047,5049,5051,5061,5063,5065,5067,5073,5075,5077,5079,5081],{},[592,5048,594],{},[638,5050,842],{},[633,5052,5053,5055],{},[592,5054,991],{},[589,5056,5057,5059],{},[638,5058,1543],{},[592,5060,996],{},[638,5062,2205],{},[592,5064,845],{},[835,5066,837],{},[633,5068,5069,5071],{},[592,5070,991],{},[592,5072,996],{},[835,5074,837],{},[592,5076,2224],{},[592,5078,830],{},[638,5080,820],{},[592,5082,1495],{},[596,5084,5085],{"encoding":598},"y = e^{-A}\\int b\\,e^{A}\\,dx + C",[573,5087,5089,5107,5216],{"className":5088,"ariaHidden":603},[602],[573,5090,5092,5095,5098,5101,5104],{"className":5091},[607],[573,5093],{"className":5094,"style":612},[611],[573,5096,594],{"className":5097,"style":618},[616,617],[573,5099],{"className":5100,"style":942},[902],[573,5102,842],{"className":5103},[946],[573,5105],{"className":5106,"style":942},[902],[573,5108,5110,5114,5149,5152,5157,5160,5163,5166,5198,5201,5204,5207,5210,5213],{"className":5109},[607],[573,5111],{"className":5112,"style":5113},[611],"height:1.1475em;vertical-align:-0.3061em;",[573,5115,5117,5120],{"className":5116},[616],[573,5118,991],{"className":5119},[616,617],[573,5121,5123],{"className":5122},[665],[573,5124,5126],{"className":5125},[669],[573,5127,5129],{"className":5128},[673],[573,5130,5132],{"className":5131,"style":4926},[677],[573,5133,5134,5137],{"style":681},[573,5135],{"className":5136,"style":686},[685],[573,5138,5140],{"className":5139},[690,691,692,693],[573,5141,5143,5146],{"className":5142},[616,693],[573,5144,1543],{"className":5145},[616,693],[573,5147,996],{"className":5148},[616,617,693],[573,5150],{"className":5151,"style":935},[902],[573,5153,2205],{"className":5154,"style":5156},[2381,2382,5155],"small-op","margin-right:0.1945em;position:relative;top:-0.0006em;",[573,5158],{"className":5159,"style":935},[902],[573,5161,845],{"className":5162},[616,617],[573,5164],{"className":5165,"style":935},[902],[573,5167,5169,5172],{"className":5168},[616],[573,5170,991],{"className":5171},[616,617],[573,5173,5175],{"className":5174},[665],[573,5176,5178],{"className":5177},[669],[573,5179,5181],{"className":5180},[673],[573,5182,5184],{"className":5183,"style":4926},[677],[573,5185,5186,5189],{"style":681},[573,5187],{"className":5188,"style":686},[685],[573,5190,5192],{"className":5191},[690,691,692,693],[573,5193,5195],{"className":5194},[616,693],[573,5196,996],{"className":5197},[616,617,693],[573,5199],{"className":5200,"style":935},[902],[573,5202,2224],{"className":5203},[616,617],[573,5205,830],{"className":5206},[616,617],[573,5208],{"className":5209,"style":903},[902],[573,5211,820],{"className":5212},[907],[573,5214],{"className":5215,"style":903},[902],[573,5217,5219,5222],{"className":5218},[607],[573,5220],{"className":5221,"style":1447},[611],[573,5223,1495],{"className":5224,"style":1510},[616,617]," ist falsch, richtig ist ",[573,5227,5229,5255],{"className":5228},[576],[573,5230,5232],{"className":5231},[580],[582,5233,5234],{"xmlns":584},[586,5235,5236,5252],{},[589,5237,5238,5240,5242],{},[592,5239,1495],{},[835,5241,837],{},[633,5243,5244,5246],{},[592,5245,991],{},[589,5247,5248,5250],{},[638,5249,1543],{},[592,5251,996],{},[596,5253,5254],{"encoding":598},"C\\,e^{-A}",[573,5256,5258],{"className":5257,"ariaHidden":603},[602],[573,5259,5261,5264,5267,5270],{"className":5260},[607],[573,5262],{"className":5263,"style":4926},[611],[573,5265,1495],{"className":5266,"style":1510},[616,617],[573,5268],{"className":5269,"style":935},[902],[573,5271,5273,5276],{"className":5272},[616],[573,5274,991],{"className":5275},[616,617],[573,5277,5279],{"className":5278},[665],[573,5280,5282],{"className":5281},[669],[573,5283,5285],{"className":5284},[673],[573,5286,5288],{"className":5287,"style":4926},[677],[573,5289,5290,5293],{"style":681},[573,5291],{"className":5292,"style":686},[685],[573,5294,5296],{"className":5295},[690,691,692,693],[573,5297,5299,5302],{"className":5298},[616,693],[573,5300,1543],{"className":5301},[616,693],[573,5303,996],{"className":5304},[616,617,693],[4615,5306,5307,5308,5443,5444,5494,5495,5547],{},"Bei ",[573,5309,5311,5339],{"className":5310},[576],[573,5312,5314],{"className":5313},[580],[582,5315,5316],{"xmlns":584},[586,5317,5318,5336],{},[589,5319,5320,5322,5324,5326,5328,5330],{},[592,5321,823],{},[638,5323,827],{"stretchy":826},[592,5325,830],{},[638,5327,833],{"stretchy":826},[638,5329,842],{},[3559,5331,5332,5334],{},[776,5333,778],{},[592,5335,830],{},[596,5337,5338],{"encoding":598},"a(x) = \\frac{1}{x}",[573,5340,5342,5369],{"className":5341,"ariaHidden":603},[602],[573,5343,5345,5348,5351,5354,5357,5360,5363,5366],{"className":5344},[607],[573,5346],{"className":5347,"style":917},[611],[573,5349,823],{"className":5350},[616,617],[573,5352,827],{"className":5353},[924],[573,5355,830],{"className":5356},[616,617],[573,5358,833],{"className":5359},[931],[573,5361],{"className":5362,"style":942},[902],[573,5364,842],{"className":5365},[946],[573,5367],{"className":5368,"style":942},[902],[573,5370,5372,5375],{"className":5371},[607],[573,5373],{"className":5374,"style":3632},[611],[573,5376,5378,5381,5440],{"className":5377},[616],[573,5379],{"className":5380},[924,3639],[573,5382,5384],{"className":5383},[3559],[573,5385,5387,5432],{"className":5386},[669,3646],[573,5388,5390,5429],{"className":5389},[673],[573,5391,5393,5407,5415],{"className":5392,"style":3653},[677],[573,5394,5395,5398],{"style":3656},[573,5396],{"className":5397,"style":3660},[685],[573,5399,5401],{"className":5400},[690,691,692,693],[573,5402,5404],{"className":5403},[616,693],[573,5405,830],{"className":5406},[616,617,693],[573,5408,5409,5412],{"style":3672},[573,5410],{"className":5411,"style":3660},[685],[573,5413],{"className":5414,"style":3680},[3679],[573,5416,5417,5420],{"style":3683},[573,5418],{"className":5419,"style":3660},[685],[573,5421,5423],{"className":5422},[690,691,692,693],[573,5424,5426],{"className":5425},[616,693],[573,5427,778],{"className":5428},[616,693],[573,5430,3700],{"className":5431},[3699],[573,5433,5435],{"className":5434},[673],[573,5436,5438],{"className":5437,"style":3707},[677],[573,5439],{},[573,5441],{"className":5442},[931,3639]," übersehen, dass die Lösung nur auf ",[573,5445,5447,5464],{"className":5446},[576],[573,5448,5450],{"className":5449},[580],[582,5451,5452],{"xmlns":584},[586,5453,5454,5462],{},[589,5455,5456,5458,5460],{},[592,5457,830],{},[638,5459,3754],{},[776,5461,1651],{},[596,5463,3759],{"encoding":598},[573,5465,5467,5485],{"className":5466,"ariaHidden":603},[602],[573,5468,5470,5473,5476,5479,5482],{"className":5469},[607],[573,5471],{"className":5472,"style":3769},[611],[573,5474,830],{"className":5475},[616,617],[573,5477],{"className":5478,"style":942},[902],[573,5480,3754],{"className":5481},[946],[573,5483],{"className":5484,"style":942},[902],[573,5486,5488,5491],{"className":5487},[607],[573,5489],{"className":5490,"style":790},[611],[573,5492,1651],{"className":5493},[616]," oder auf ",[573,5496,5498,5517],{"className":5497},[576],[573,5499,5501],{"className":5500},[580],[582,5502,5503],{"xmlns":584},[586,5504,5505,5514],{},[589,5506,5507,5509,5512],{},[592,5508,830],{},[638,5510,5511],{},"\u003C",[776,5513,1651],{},[596,5515,5516],{"encoding":598},"x \u003C 0",[573,5518,5520,5538],{"className":5519,"ariaHidden":603},[602],[573,5521,5523,5526,5529,5532,5535],{"className":5522},[607],[573,5524],{"className":5525,"style":3769},[611],[573,5527,830],{"className":5528},[616,617],[573,5530],{"className":5531,"style":942},[902],[573,5533,5511],{"className":5534},[946],[573,5536],{"className":5537,"style":942},[902],[573,5539,5541,5544],{"className":5540},[607],[573,5542],{"className":5543,"style":790},[611],[573,5545,1651],{"className":5546},[616]," gilt.",{"title":5549,"searchDepth":5550,"depth":5550,"links":5551},"",2,[5552,5553,5554],{"id":561,"depth":5550,"text":562},{"id":1808,"depth":5550,"text":1809},{"id":4609,"depth":5550,"text":4610},[5556,5558,5561,5565,5567,5570,5572],{"lhs":5557,"rhs":1841},"-2*C*exp(-2*x) + 2*(2 + C*exp(-2*x))",{"lhs":5559,"rhs":5560},"exp(-2*x)*(2*exp(2*x) + C)","2 + C*exp(-2*x)",{"lhs":5562,"rhs":1651,"where":5563},"2 + C*exp(-2*0)",{"C":5564},-2,{"lhs":5566,"rhs":1841},"4*exp(-2*x) + 2*(2 - 2*exp(-2*x))",{"lhs":5568,"rhs":5569},"round(2 - 2*exp(-2), 4)","1.7293",{"lhs":5571,"rhs":830},"(2*x\u002F3 - C\u002Fx^2) + (x^2\u002F3 + C\u002Fx)\u002Fx",{"lhs":5573,"rhs":5574},"(x^3\u002F3 + C)\u002Fx","x^2\u002F3 + C\u002Fx","a,\\ b \\text{ stetig},\\ A'(x) = a(x)","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>a\u003C\u002Fmi>\u003Cmo 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separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">,\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:0.3em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\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","linear-ode-first-order","y' + a(x)\\,y = b(x) \\;\\Rightarrow\\; y(x) = e^{-A(x)} \\left( \\int b(x)\\,e^{A(x)}\\,dx + C \\right)","\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>\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 stretchy=\"false\">)\u003C\u002Fmo>\u003Cmtext>  \u003C\u002Fmtext>\u003Cmo>⇒\u003C\u002Fmo>\u003Cmtext>  \u003C\u002Fmtext>\u003Cmi>y\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmo 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