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Der Exponentialansatz liefert dann nur eine Lösung ",[568,1106,1108,1132],{"className":1107},[571],[568,1109,1111],{"className":1110},[575],[577,1112,1113],{"xmlns":579},[581,1114,1115,1129],{},[584,1116,1117],{},[587,1118,1119,1122],{},[590,1120,1121],{},"e",[584,1123,1124,1126],{},[590,1125,975],{},[590,1127,1128],{},"x",[636,1130,1131],{"encoding":638},"e^{\\lambda x}",[568,1133,1135],{"className":1134,"ariaHidden":644},[643],[568,1136,1138,1142],{"className":1137},[648],[568,1139],{"className":1140,"style":1141},[652],"height:0.8491em;",[568,1143,1145,1148],{"className":1144},[657],[568,1146,1121],{"className":1147},[657,661],[568,1149,1151],{"className":1150},[666],[568,1152,1154],{"className":1153},[670],[568,1155,1157],{"className":1156},[674],[568,1158,1160],{"className":1159,"style":1141},[678],[568,1161,1162,1165],{"style":682},[568,1163],{"className":1164,"style":687},[686],[568,1166,1168],{"className":1167},[691,692,693,694],[568,1169,1171,1174],{"className":1170},[657,694],[568,1172,975],{"className":1173},[657,661,694],[568,1175,1128],{"className":1176},[657,661,694],", für die allgemeine Lösung braucht man aber zwei unabhängige.",[564,1179,1180,1181,1260],{},"Die zweite Lösung ist ",[568,1182,1184,1210],{"className":1183},[571],[568,1185,1187],{"className":1186},[575],[577,1188,1189],{"xmlns":579},[581,1190,1191,1207],{},[584,1192,1193,1195,1197],{},[590,1194,1128],{},[609,1196,611],{},[587,1198,1199,1201],{},[590,1200,1121],{},[584,1202,1203,1205],{},[590,1204,975],{},[590,1206,1128],{},[636,1208,1209],{"encoding":638},"x\\,e^{\\lambda x}",[568,1211,1213],{"className":1212,"ariaHidden":644},[643],[568,1214,1216,1219,1222,1225],{"className":1215},[648],[568,1217],{"className":1218,"style":1141},[652],[568,1220,1128],{"className":1221},[657,661],[568,1223],{"className":1224,"style":726},[705],[568,1226,1228,1231],{"className":1227},[657],[568,1229,1121],{"className":1230},[657,661],[568,1232,1234],{"className":1233},[666],[568,1235,1237],{"className":1236},[670],[568,1238,1240],{"className":1239},[674],[568,1241,1243],{"className":1242,"style":1141},[678],[568,1244,1245,1248],{"style":682},[568,1246],{"className":1247,"style":687},[686],[568,1249,1251],{"className":1250},[691,692,693,694],[568,1252,1254,1257],{"className":1253},[657,694],[568,1255,975],{"className":1256},[657,661,694],[568,1258,1128],{"className":1259},[657,661,694],". Setzt man sie ein, ergibt sich",[568,1262,1265],{"className":1263},[1264],"katex-display",[568,1266,1268,1411],{"className":1267},[571],[568,1269,1271],{"className":1270},[575],[577,1272,1274],{"xmlns":579,"display":1273},"block",[581,1275,1276,1408],{},[584,1277,1278,1282,1284,1286,1296,1307,1309,1311,1313,1315,1317,1319,1329,1335,1337,1339,1341,1343,1345,1355,1357,1359,1362,1368,1370,1372,1374,1376,1378,1380,1382,1384,1386,1388,1390,1392,1394,1396,1398],{},[596,1279,1281],{"fence":644,"stretchy":644,"minsize":1280,"maxsize":1280},"1.2em","(",[590,1283,1128],{},[609,1285,611],{},[587,1287,1288,1290],{},[590,1289,1121],{},[584,1291,1292,1294],{},[590,1293,975],{},[590,1295,1128],{},[587,1297,1298,1301],{},[596,1299,1300],{"fence":644,"stretchy":644,"minsize":1280,"maxsize":1280},")",[584,1302,1303,1305],{},[596,1304,599],{"mathvariant":598},[596,1306,599],{"mathvariant":598},[596,1308,604],{},[590,1310,607],{},[609,1312,611],{},[596,1314,1281],{"fence":644,"stretchy":644,"minsize":1280,"maxsize":1280},[590,1316,1128],{},[609,1318,611],{},[587,1320,1321,1323],{},[590,1322,1121],{},[584,1324,1325,1327],{},[590,1326,975],{},[590,1328,1128],{},[587,1330,1331,1333],{},[596,1332,1300],{"fence":644,"stretchy":644,"minsize":1280,"maxsize":1280},[596,1334,599],{"mathvariant":598,"lspace":618,"rspace":618},[596,1336,604],{},[590,1338,623],{},[609,1340,611],{},[590,1342,1128],{},[609,1344,611],{},[587,1346,1347,1349],{},[590,1348,1121],{},[584,1350,1351,1353],{},[590,1352,975],{},[590,1354,1128],{},[596,1356,630],{},[596,1358,1281],{"fence":644,"stretchy":644,"minsize":1280,"maxsize":1280},[596,1360,1281],{"stretchy":1361},"false",[587,1363,1364,1366],{},[590,1365,975],{},[632,1367,884],{},[596,1369,604],{},[590,1371,607],{},[590,1373,975],{},[596,1375,604],{},[590,1377,623],{},[596,1379,1300],{"stretchy":1361},[609,1381,611],{},[590,1383,1128],{},[596,1385,604],{},[632,1387,884],{},[590,1389,975],{},[596,1391,604],{},[590,1393,607],{},[596,1395,1300],{"fence":644,"stretchy":644,"minsize":1280,"maxsize":1280},[609,1397,611],{},[587,1399,1400,1402],{},[590,1401,1121],{},[584,1403,1404,1406],{},[590,1405,975],{},[590,1407,1128],{},[636,1409,1410],{"encoding":638},"\\bigl(x\\,e^{\\lambda x}\\bigr)'' + a\\,\\bigl(x\\,e^{\\lambda x}\\bigr)' + b\\,x\\,e^{\\lambda x} = \\bigl((\\lambda^2 + a\\lambda + b)\\,x + 2\\lambda + a\\bigr)\\,e^{\\lambda x}",[568,1412,1414,1518,1621,1683,1738,1758,1786,1807],{"className":1413,"ariaHidden":644},[643],[568,1415,1417,1421,1429,1432,1435,1472,1509,1512,1515],{"className":1416},[648],[568,1418],{"className":1419,"style":1420},[652],"height:1.3418em;vertical-align:-0.35em;",[568,1422,1424],{"className":1423},[1028],[568,1425,1281],{"className":1426},[1427,1428],"delimsizing","size1",[568,1430,1128],{"className":1431},[657,661],[568,1433],{"className":1434,"style":726},[705],[568,1436,1438,1441],{"className":1437},[657],[568,1439,1121],{"className":1440},[657,661],[568,1442,1444],{"className":1443},[666],[568,1445,1447],{"className":1446},[670],[568,1448,1450],{"className":1449},[674],[568,1451,1454],{"className":1452,"style":1453},[678],"height:0.8991em;",[568,1455,1457,1460],{"style":1456},"top:-3.113em;margin-right:0.05em;",[568,1458],{"className":1459,"style":687},[686],[568,1461,1463],{"className":1462},[691,692,693,694],[568,1464,1466,1469],{"className":1465},[657,694],[568,1467,975],{"className":1468},[657,661,694],[568,1470,1128],{"className":1471},[657,661,694],[568,1473,1475,1481],{"className":1474},[1103],[568,1476,1478],{"className":1477},[1103],[568,1479,1300],{"className":1480},[1427,1428],[568,1482,1484],{"className":1483},[666],[568,1485,1487],{"className":1486},[670],[568,1488,1490],{"className":1489},[674],[568,1491,1494],{"className":1492,"style":1493},[678],"height:0.9918em;",[568,1495,1497,1500],{"style":1496},"top:-3.3029em;margin-right:0.05em;",[568,1498],{"className":1499,"style":687},[686],[568,1501,1503],{"className":1502},[691,692,693,694],[568,1504,1506],{"className":1505},[657,694],[568,1507,701],{"className":1508},[657,694],[568,1510],{"className":1511,"style":706},[705],[568,1513,604],{"className":1514},[710],[568,1516],{"className":1517,"style":706},[705],[568,1519,1521,1524,1527,1530,1536,1539,1542,1577,1612,1615,1618],{"className":1520},[648],[568,1522],{"className":1523,"style":1420},[652],[568,1525,607],{"className":1526},[657,661],[568,1528],{"className":1529,"style":726},[705],[568,1531,1533],{"className":1532},[1028],[568,1534,1281],{"className":1535},[1427,1428],[568,1537,1128],{"className":1538},[657,661],[568,1540],{"className":1541,"style":726},[705],[568,1543,1545,1548],{"className":1544},[657],[568,1546,1121],{"className":1547},[657,661],[568,1549,1551],{"className":1550},[666],[568,1552,1554],{"className":1553},[670],[568,1555,1557],{"className":1556},[674],[568,1558,1560],{"className":1559,"style":1453},[678],[568,1561,1562,1565],{"style":1456},[568,1563],{"className":1564,"style":687},[686],[568,1566,1568],{"className":1567},[691,692,693,694],[568,1569,1571,1574],{"className":1570},[657,694],[568,1572,975],{"className":1573},[657,661,694],[568,1575,1128],{"className":1576},[657,661,694],[568,1578,1580,1586],{"className":1579},[1103],[568,1581,1583],{"className":1582},[1103],[568,1584,1300],{"className":1585},[1427,1428],[568,1587,1589],{"className":1588},[666],[568,1590,1592],{"className":1591},[670],[568,1593,1595],{"className":1594},[674],[568,1596,1598],{"className":1597,"style":1493},[678],[568,1599,1600,1603],{"style":1496},[568,1601],{"className":1602,"style":687},[686],[568,1604,1606],{"className":1605},[691,692,693,694],[568,1607,1609],{"className":1608},[657,694],[568,1610,599],{"className":1611},[657,694],[568,1613],{"className":1614,"style":706},[705],[568,1616,604],{"className":1617},[710],[568,1619],{"className":1620,"style":706},[705],[568,1622,1624,1627,1630,1633,1636,1639,1674,1677,1680],{"className":1623},[648],[568,1625],{"className":1626,"style":1453},[652],[568,1628,623],{"className":1629},[657,661],[568,1631],{"className":1632,"style":726},[705],[568,1634,1128],{"className":1635},[657,661],[568,1637],{"className":1638,"style":726},[705],[568,1640,1642,1645],{"className":1641},[657],[568,1643,1121],{"className":1644},[657,661],[568,1646,1648],{"className":1647},[666],[568,1649,1651],{"className":1650},[670],[568,1652,1654],{"className":1653},[674],[568,1655,1657],{"className":1656,"style":1453},[678],[568,1658,1659,1662],{"style":1456},[568,1660],{"className":1661,"style":687},[686],[568,1663,1665],{"className":1664},[691,692,693,694],[568,1666,1668,1671],{"className":1667},[657,694],[568,1669,975],{"className":1670},[657,661,694],[568,1672,1128],{"className":1673},[657,661,694],[568,1675],{"className":1676,"style":787},[705],[568,1678,630],{"className":1679},[791],[568,1681],{"className":1682,"style":787},[705],[568,1684,1686,1690,1696,1699,1729,1732,1735],{"className":1685},[648],[568,1687],{"className":1688,"style":1689},[652],"height:1.2141em;vertical-align:-0.35em;",[568,1691,1693],{"className":1692},[1028],[568,1694,1281],{"className":1695},[1427,1428],[568,1697,1281],{"className":1698},[1028],[568,1700,1702,1705],{"className":1701},[657],[568,1703,975],{"className":1704},[657,661],[568,1706,1708],{"className":1707},[666],[568,1709,1711],{"className":1710},[670],[568,1712,1714],{"className":1713},[674],[568,1715,1718],{"className":1716,"style":1717},[678],"height:0.8641em;",[568,1719,1720,1723],{"style":1456},[568,1721],{"className":1722,"style":687},[686],[568,1724,1726],{"className":1725},[691,692,693,694],[568,1727,884],{"className":1728},[657,694],[568,1730],{"className":1731,"style":706},[705],[568,1733,604],{"className":1734},[710],[568,1736],{"className":1737,"style":706},[705],[568,1739,1741,1745,1749,1752,1755],{"className":1740},[648],[568,1742],{"className":1743,"style":1744},[652],"height:0.7778em;vertical-align:-0.0833em;",[568,1746,1748],{"className":1747},[657,661],"aλ",[568,1750],{"className":1751,"style":706},[705],[568,1753,604],{"className":1754},[710],[568,1756],{"className":1757,"style":706},[705],[568,1759,1761,1765,1768,1771,1774,1777,1780,1783],{"className":1760},[648],[568,1762],{"className":1763,"style":1764},[652],"height:1em;vertical-align:-0.25em;",[568,1766,623],{"className":1767},[657,661],[568,1769,1300],{"className":1770},[1103],[568,1772],{"className":1773,"style":726},[705],[568,1775,1128],{"className":1776},[657,661],[568,1778],{"className":1779,"style":706},[705],[568,1781,604],{"className":1782},[710],[568,1784],{"className":1785,"style":706},[705],[568,1787,1789,1792,1795,1798,1801,1804],{"className":1788},[648],[568,1790],{"className":1791,"style":1744},[652],[568,1793,884],{"className":1794},[657],[568,1796,975],{"className":1797},[657,661],[568,1799],{"className":1800,"style":706},[705],[568,1802,604],{"className":1803},[710],[568,1805],{"className":1806,"style":706},[705],[568,1808,1810,1814,1817,1823,1826],{"className":1809},[648],[568,1811],{"className":1812,"style":1813},[652],"height:1.2491em;vertical-align:-0.35em;",[568,1815,607],{"className":1816},[657,661],[568,1818,1820],{"className":1819},[1103],[568,1821,1300],{"className":1822},[1427,1428],[568,1824],{"className":1825,"style":726},[705],[568,1827,1829,1832],{"className":1828},[657],[568,1830,1121],{"className":1831},[657,661],[568,1833,1835],{"className":1834},[666],[568,1836,1838],{"className":1837},[670],[568,1839,1841],{"className":1840},[674],[568,1842,1844],{"className":1843,"style":1453},[678],[568,1845,1846,1849],{"style":1456},[568,1847],{"className":1848,"style":687},[686],[568,1850,1852],{"className":1851},[691,692,693,694],[568,1853,1855,1858],{"className":1854},[657,694],[568,1856,975],{"className":1857},[657,661,694],[568,1859,1128],{"className":1860},[657,661,694],[564,1862,1863,1864,1893,1894,2018],{},"Beide Klammerterme sind null: der erste, weil ",[568,1865,1867,1881],{"className":1866},[571],[568,1868,1870],{"className":1869},[575],[577,1871,1872],{"xmlns":579},[581,1873,1874,1878],{},[584,1875,1876],{},[590,1877,975],{},[636,1879,1880],{"encoding":638},"\\lambda",[568,1882,1884],{"className":1883,"ariaHidden":644},[643],[568,1885,1887,1890],{"className":1886},[648],[568,1888],{"className":1889,"style":861},[652],[568,1891,975],{"className":1892},[657,661]," Nullstelle ist, der zweite wegen ",[568,1895,1897,1920],{"className":1896},[571],[568,1898,1900],{"className":1899},[575],[577,1901,1902],{"xmlns":579},[581,1903,1904,1918],{},[584,1905,1906,1908,1910,1912],{},[590,1907,975],{},[596,1909,630],{},[596,1911,980],{},[982,1913,1914,1916],{},[590,1915,607],{},[632,1917,884],{},[636,1919,990],{"encoding":638},[568,1921,1923,1941],{"className":1922,"ariaHidden":644},[643],[568,1924,1926,1929,1932,1935,1938],{"className":1925},[648],[568,1927],{"className":1928,"style":861},[652],[568,1930,975],{"className":1931},[657,661],[568,1933],{"className":1934,"style":787},[705],[568,1936,630],{"className":1937},[791],[568,1939],{"className":1940,"style":787},[705],[568,1942,1944,1947,1950],{"className":1943},[648],[568,1945],{"className":1946,"style":1018},[652],[568,1948,980],{"className":1949},[657],[568,1951,1953,1956,2015],{"className":1952},[657],[568,1954],{"className":1955},[1028,1029],[568,1957,1959],{"className":1958},[982],[568,1960,1962,2007],{"className":1961},[670,1036],[568,1963,1965,2004],{"className":1964},[674],[568,1966,1968,1982,1990],{"className":1967,"style":1043},[678],[568,1969,1970,1973],{"style":1046},[568,1971],{"className":1972,"style":1050},[686],[568,1974,1976],{"className":1975},[691,692,693,694],[568,1977,1979],{"className":1978},[657,694],[568,1980,884],{"className":1981},[657,694],[568,1983,1984,1987],{"style":1062},[568,1985],{"className":1986,"style":1050},[686],[568,1988],{"className":1989,"style":1070},[1069],[568,1991,1992,1995],{"style":1073},[568,1993],{"className":1994,"style":1050},[686],[568,1996,1998],{"className":1997},[691,692,693,694],[568,1999,2001],{"className":2000},[657,694],[568,2002,607],{"className":2003},[657,661,694],[568,2005,1090],{"className":2006},[1089],[568,2008,2010],{"className":2009},[674],[568,2011,2013],{"className":2012,"style":1097},[678],[568,2014],{},[568,2016],{"className":2017},[1103,1029],". Genau hier braucht man die doppelte Nullstelle.",[564,2020,2021,2022,835,2134,2277,2278,2416,2417,2619,2620,2622],{},"Die Anfangswerte ",[568,2023,2025,2054],{"className":2024},[571],[568,2026,2028],{"className":2027},[575],[577,2029,2030],{"xmlns":579},[581,2031,2032,2051],{},[584,2033,2034,2036,2038,2040,2042,2044],{},[590,2035,592],{},[596,2037,1281],{"stretchy":1361},[632,2039,634],{},[596,2041,1300],{"stretchy":1361},[596,2043,630],{},[2045,2046,2047,2049],"msub",{},[590,2048,592],{},[632,2050,634],{},[636,2052,2053],{"encoding":638},"y(0) = y_0",[568,2055,2057,2084],{"className":2056,"ariaHidden":644},[643],[568,2058,2060,2063,2066,2069,2072,2075,2078,2081],{"className":2059},[648],[568,2061],{"className":2062,"style":1764},[652],[568,2064,592],{"className":2065,"style":662},[657,661],[568,2067,1281],{"className":2068},[1028],[568,2070,634],{"className":2071},[657],[568,2073,1300],{"className":2074},[1103],[568,2076],{"className":2077,"style":787},[705],[568,2079,630],{"className":2080},[791],[568,2082],{"className":2083,"style":787},[705],[568,2085,2087,2091],{"className":2086},[648],[568,2088],{"className":2089,"style":2090},[652],"height:0.625em;vertical-align:-0.1944em;",[568,2092,2094,2097],{"className":2093},[657],[568,2095,592],{"className":2096,"style":662},[657,661],[568,2098,2100],{"className":2099},[666],[568,2101,2103,2125],{"className":2102},[670,1036],[568,2104,2106,2122],{"className":2105},[674],[568,2107,2110],{"className":2108,"style":2109},[678],"height:0.3011em;",[568,2111,2113,2116],{"style":2112},"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;",[568,2114],{"className":2115,"style":687},[686],[568,2117,2119],{"className":2118},[691,692,693,694],[568,2120,634],{"className":2121},[657,694],[568,2123,1090],{"className":2124},[1089],[568,2126,2128],{"className":2127},[674],[568,2129,2132],{"className":2130,"style":2131},[678],"height:0.15em;",[568,2133],{},[568,2135,2137,2170],{"className":2136},[571],[568,2138,2140],{"className":2139},[575],[577,2141,2142],{"xmlns":579},[581,2143,2144,2167],{},[584,2145,2146,2152,2154,2156,2158,2160],{},[587,2147,2148,2150],{},[590,2149,592],{},[596,2151,599],{"mathvariant":598,"lspace":618,"rspace":618},[596,2153,1281],{"stretchy":1361},[632,2155,634],{},[596,2157,1300],{"stretchy":1361},[596,2159,630],{},[2045,2161,2162,2165],{},[590,2163,2164],{},"v",[632,2166,634],{},[636,2168,2169],{"encoding":638},"y'(0) = v_0",[568,2171,2173,2230],{"className":2172,"ariaHidden":644},[643],[568,2174,2176,2180,2212,2215,2218,2221,2224,2227],{"className":2175},[648],[568,2177],{"className":2178,"style":2179},[652],"height:1.0019em;vertical-align:-0.25em;",[568,2181,2183,2186],{"className":2182},[657],[568,2184,592],{"className":2185,"style":662},[657,661],[568,2187,2189],{"className":2188},[666],[568,2190,2192],{"className":2191},[670],[568,2193,2195],{"className":2194},[674],[568,2196,2198],{"className":2197,"style":679},[678],[568,2199,2200,2203],{"style":682},[568,2201],{"className":2202,"style":687},[686],[568,2204,2206],{"className":2205},[691,692,693,694],[568,2207,2209],{"className":2208},[657,694],[568,2210,599],{"className":2211},[657,694],[568,2213,1281],{"className":2214},[1028],[568,2216,634],{"className":2217},[657],[568,2219,1300],{"className":2220},[1103],[568,2222],{"className":2223,"style":787},[705],[568,2225,630],{"className":2226},[791],[568,2228],{"className":2229,"style":787},[705],[568,2231,2233,2237],{"className":2232},[648],[568,2234],{"className":2235,"style":2236},[652],"height:0.5806em;vertical-align:-0.15em;",[568,2238,2240,2243],{"className":2239},[657],[568,2241,2164],{"className":2242,"style":662},[657,661],[568,2244,2246],{"className":2245},[666],[568,2247,2249,2269],{"className":2248},[670,1036],[568,2250,2252,2266],{"className":2251},[674],[568,2253,2255],{"className":2254,"style":2109},[678],[568,2256,2257,2260],{"style":2112},[568,2258],{"className":2259,"style":687},[686],[568,2261,2263],{"className":2262},[691,692,693,694],[568,2264,634],{"className":2265},[657,694],[568,2267,1090],{"className":2268},[1089],[568,2270,2272],{"className":2271},[674],[568,2273,2275],{"className":2274,"style":2131},[678],[568,2276],{}," ergeben ",[568,2279,2281,2309],{"className":2280},[571],[568,2282,2284],{"className":2283},[575],[577,2285,2286],{"xmlns":579},[581,2287,2288,2306],{},[584,2289,2290,2298,2300],{},[2045,2291,2292,2295],{},[590,2293,2294],{},"C",[632,2296,2297],{},"1",[596,2299,630],{},[2045,2301,2302,2304],{},[590,2303,592],{},[632,2305,634],{},[636,2307,2308],{"encoding":638},"C_1 = y_0",[568,2310,2312,2370],{"className":2311,"ariaHidden":644},[643],[568,2313,2315,2319,2361,2364,2367],{"className":2314},[648],[568,2316],{"className":2317,"style":2318},[652],"height:0.8333em;vertical-align:-0.15em;",[568,2320,2322,2326],{"className":2321},[657],[568,2323,2294],{"className":2324,"style":2325},[657,661],"margin-right:0.0715em;",[568,2327,2329],{"className":2328},[666],[568,2330,2332,2353],{"className":2331},[670,1036],[568,2333,2335,2350],{"className":2334},[674],[568,2336,2338],{"className":2337,"style":2109},[678],[568,2339,2341,2344],{"style":2340},"top:-2.55em;margin-left:-0.0715em;margin-right:0.05em;",[568,2342],{"className":2343,"style":687},[686],[568,2345,2347],{"className":2346},[691,692,693,694],[568,2348,2297],{"className":2349},[657,694],[568,2351,1090],{"className":2352},[1089],[568,2354,2356],{"className":2355},[674],[568,2357,2359],{"className":2358,"style":2131},[678],[568,2360],{},[568,2362],{"className":2363,"style":787},[705],[568,2365,630],{"className":2366},[791],[568,2368],{"className":2369,"style":787},[705],[568,2371,2373,2376],{"className":2372},[648],[568,2374],{"className":2375,"style":2090},[652],[568,2377,2379,2382],{"className":2378},[657],[568,2380,592],{"className":2381,"style":662},[657,661],[568,2383,2385],{"className":2384},[666],[568,2386,2388,2408],{"className":2387},[670,1036],[568,2389,2391,2405],{"className":2390},[674],[568,2392,2394],{"className":2393,"style":2109},[678],[568,2395,2396,2399],{"style":2112},[568,2397],{"className":2398,"style":687},[686],[568,2400,2402],{"className":2401},[691,692,693,694],[568,2403,634],{"className":2404},[657,694],[568,2406,1090],{"className":2407},[1089],[568,2409,2411],{"className":2410},[674],[568,2412,2414],{"className":2413,"style":2131},[678],[568,2415],{}," und ",[568,2418,2420,2456],{"className":2419},[571],[568,2421,2423],{"className":2422},[575],[577,2424,2425],{"xmlns":579},[581,2426,2427,2453],{},[584,2428,2429,2435,2437,2439,2445,2447],{},[2045,2430,2431,2433],{},[590,2432,2294],{},[632,2434,884],{},[596,2436,604],{},[590,2438,975],{},[2045,2440,2441,2443],{},[590,2442,2294],{},[632,2444,2297],{},[596,2446,630],{},[2045,2448,2449,2451],{},[590,2450,2164],{},[632,2452,634],{},[636,2454,2455],{"encoding":638},"C_2 + \\lambda C_1 = v_0",[568,2457,2459,2514,2573],{"className":2458,"ariaHidden":644},[643],[568,2460,2462,2465,2505,2508,2511],{"className":2461},[648],[568,2463],{"className":2464,"style":2318},[652],[568,2466,2468,2471],{"className":2467},[657],[568,2469,2294],{"className":2470,"style":2325},[657,661],[568,2472,2474],{"className":2473},[666],[568,2475,2477,2497],{"className":2476},[670,1036],[568,2478,2480,2494],{"className":2479},[674],[568,2481,2483],{"className":2482,"style":2109},[678],[568,2484,2485,2488],{"style":2340},[568,2486],{"className":2487,"style":687},[686],[568,2489,2491],{"className":2490},[691,692,693,694],[568,2492,884],{"className":2493},[657,694],[568,2495,1090],{"className":2496},[1089],[568,2498,2500],{"className":2499},[674],[568,2501,2503],{"className":2502,"style":2131},[678],[568,2504],{},[568,2506],{"className":2507,"style":706},[705],[568,2509,604],{"className":2510},[710],[568,2512],{"className":2513,"style":706},[705],[568,2515,2517,2521,2524,2564,2567,2570],{"className":2516},[648],[568,2518],{"className":2519,"style":2520},[652],"height:0.8444em;vertical-align:-0.15em;",[568,2522,975],{"className":2523},[657,661],[568,2525,2527,2530],{"className":2526},[657],[568,2528,2294],{"className":2529,"style":2325},[657,661],[568,2531,2533],{"className":2532},[666],[568,2534,2536,2556],{"className":2535},[670,1036],[568,2537,2539,2553],{"className":2538},[674],[568,2540,2542],{"className":2541,"style":2109},[678],[568,2543,2544,2547],{"style":2340},[568,2545],{"className":2546,"style":687},[686],[568,2548,2550],{"className":2549},[691,692,693,694],[568,2551,2297],{"className":2552},[657,694],[568,2554,1090],{"className":2555},[1089],[568,2557,2559],{"className":2558},[674],[568,2560,2562],{"className":2561,"style":2131},[678],[568,2563],{},[568,2565],{"className":2566,"style":787},[705],[568,2568,630],{"className":2569},[791],[568,2571],{"className":2572,"style":787},[705],[568,2574,2576,2579],{"className":2575},[648],[568,2577],{"className":2578,"style":2236},[652],[568,2580,2582,2585],{"className":2581},[657],[568,2583,2164],{"className":2584,"style":662},[657,661],[568,2586,2588],{"className":2587},[666],[568,2589,2591,2611],{"className":2590},[670,1036],[568,2592,2594,2608],{"className":2593},[674],[568,2595,2597],{"className":2596,"style":2109},[678],[568,2598,2599,2602],{"style":2112},[568,2600],{"className":2601,"style":687},[686],[568,2603,2605],{"className":2604},[691,692,693,694],[568,2606,634],{"className":2607},[657,694],[568,2609,1090],{"className":2610},[1089],[568,2612,2614],{"className":2613},[674],[568,2615,2617],{"className":2616,"style":2131},[678],[568,2618],{},". In der Physik heißt dieser Fall ",[957,2621,551],{},": Die Lösung kehrt so schnell wie möglich ohne Überschwingen in die Ruhelage zurück.",[559,2624,2626],{"id":2625},"beispiele","Beispiele",[564,2628,2629,2805,2806,2416,2872,2971,2972,3166,3167,3224],{},[568,2630,2632,2674],{"className":2631},[571],[568,2633,2635],{"className":2634},[575],[577,2636,2637],{"xmlns":579},[581,2638,2639,2671],{},[584,2640,2641,2651,2653,2655,2661,2663,2665,2667,2669],{},[587,2642,2643,2645],{},[590,2644,592],{},[584,2646,2647,2649],{},[596,2648,599],{"mathvariant":598},[596,2650,599],{"mathvariant":598},[596,2652,604],{},[632,2654,889],{},[587,2656,2657,2659],{},[590,2658,592],{},[596,2660,599],{"mathvariant":598,"lspace":618,"rspace":618},[596,2662,604],{},[632,2664,889],{},[590,2666,592],{},[596,2668,630],{},[632,2670,634],{},[636,2672,2673],{"encoding":638},"y'' + 4y' + 4y = 0",[568,2675,2677,2724,2774,2796],{"className":2676,"ariaHidden":644},[643],[568,2678,2680,2683,2715,2718,2721],{"className":2679},[648],[568,2681],{"className":2682,"style":653},[652],[568,2684,2686,2689],{"className":2685},[657],[568,2687,592],{"className":2688,"style":662},[657,661],[568,2690,2692],{"className":2691},[666],[568,2693,2695],{"className":2694},[670],[568,2696,2698],{"className":2697},[674],[568,2699,2701],{"className":2700,"style":679},[678],[568,2702,2703,2706],{"style":682},[568,2704],{"className":2705,"style":687},[686],[568,2707,2709],{"className":2708},[691,692,693,694],[568,2710,2712],{"className":2711},[657,694],[568,2713,701],{"className":2714},[657,694],[568,2716],{"className":2717,"style":706},[705],[568,2719,604],{"className":2720},[710],[568,2722],{"className":2723,"style":706},[705],[568,2725,2727,2730,2733,2765,2768,2771],{"className":2726},[648],[568,2728],{"className":2729,"style":653},[652],[568,2731,889],{"className":2732},[657],[568,2734,2736,2739],{"className":2735},[657],[568,2737,592],{"className":2738,"style":662},[657,661],[568,2740,2742],{"className":2741},[666],[568,2743,2745],{"className":2744},[670],[568,2746,2748],{"className":2747},[674],[568,2749,2751],{"className":2750,"style":679},[678],[568,2752,2753,2756],{"style":682},[568,2754],{"className":2755,"style":687},[686],[568,2757,2759],{"className":2758},[691,692,693,694],[568,2760,2762],{"className":2761},[657,694],[568,2763,599],{"className":2764},[657,694],[568,2766],{"className":2767,"style":706},[705],[568,2769,604],{"className":2770},[710],[568,2772],{"className":2773,"style":706},[705],[568,2775,2777,2781,2784,2787,2790,2793],{"className":2776},[648],[568,2778],{"className":2779,"style":2780},[652],"height:0.8389em;vertical-align:-0.1944em;",[568,2782,889],{"className":2783},[657],[568,2785,592],{"className":2786,"style":662},[657,661],[568,2788],{"className":2789,"style":787},[705],[568,2791,630],{"className":2792},[791],[568,2794],{"className":2795,"style":787},[705],[568,2797,2799,2802],{"className":2798},[648],[568,2800],{"className":2801,"style":801},[652],[568,2803,634],{"className":2804},[657]," mit ",[568,2807,2809,2833],{"className":2808},[571],[568,2810,2812],{"className":2811},[575],[577,2813,2814],{"xmlns":579},[581,2815,2816,2830],{},[584,2817,2818,2820,2822,2824,2826,2828],{},[590,2819,592],{},[596,2821,1281],{"stretchy":1361},[632,2823,634],{},[596,2825,1300],{"stretchy":1361},[596,2827,630],{},[632,2829,2297],{},[636,2831,2832],{"encoding":638},"y(0) = 1",[568,2834,2836,2863],{"className":2835,"ariaHidden":644},[643],[568,2837,2839,2842,2845,2848,2851,2854,2857,2860],{"className":2838},[648],[568,2840],{"className":2841,"style":1764},[652],[568,2843,592],{"className":2844,"style":662},[657,661],[568,2846,1281],{"className":2847},[1028],[568,2849,634],{"className":2850},[657],[568,2852,1300],{"className":2853},[1103],[568,2855],{"className":2856,"style":787},[705],[568,2858,630],{"className":2859},[791],[568,2861],{"className":2862,"style":787},[705],[568,2864,2866,2869],{"className":2865},[648],[568,2867],{"className":2868,"style":801},[652],[568,2870,2297],{"className":2871},[657],[568,2873,2875,2903],{"className":2874},[571],[568,2876,2878],{"className":2877},[575],[577,2879,2880],{"xmlns":579},[581,2881,2882,2900],{},[584,2883,2884,2890,2892,2894,2896,2898],{},[587,2885,2886,2888],{},[590,2887,592],{},[596,2889,599],{"mathvariant":598,"lspace":618,"rspace":618},[596,2891,1281],{"stretchy":1361},[632,2893,634],{},[596,2895,1300],{"stretchy":1361},[596,2897,630],{},[632,2899,634],{},[636,2901,2902],{"encoding":638},"y'(0) = 0",[568,2904,2906,2962],{"className":2905,"ariaHidden":644},[643],[568,2907,2909,2912,2944,2947,2950,2953,2956,2959],{"className":2908},[648],[568,2910],{"className":2911,"style":2179},[652],[568,2913,2915,2918],{"className":2914},[657],[568,2916,592],{"className":2917,"style":662},[657,661],[568,2919,2921],{"className":2920},[666],[568,2922,2924],{"className":2923},[670],[568,2925,2927],{"className":2926},[674],[568,2928,2930],{"className":2929,"style":679},[678],[568,2931,2932,2935],{"style":682},[568,2933],{"className":2934,"style":687},[686],[568,2936,2938],{"className":2937},[691,692,693,694],[568,2939,2941],{"className":2940},[657,694],[568,2942,599],{"className":2943},[657,694],[568,2945,1281],{"className":2946},[1028],[568,2948,634],{"className":2949},[657],[568,2951,1300],{"className":2952},[1103],[568,2954],{"className":2955,"style":787},[705],[568,2957,630],{"className":2958},[791],[568,2960],{"className":2961,"style":787},[705],[568,2963,2965,2968],{"className":2964},[648],[568,2966],{"className":2967,"style":801},[652],[568,2969,634],{"className":2970},[657],". Es ist ",[568,2973,2975,3019],{"className":2974},[571],[568,2976,2978],{"className":2977},[575],[577,2979,2980],{"xmlns":579},[581,2981,2982,3016],{},[584,2983,2984,2990,2992,2994,2996,2998,3000,3002,3004,3006,3008,3010],{},[587,2985,2986,2988],{},[590,2987,975],{},[632,2989,884],{},[596,2991,604],{},[632,2993,889],{},[590,2995,975],{},[596,2997,604],{},[632,2999,889],{},[596,3001,630],{},[596,3003,1281],{"stretchy":1361},[590,3005,975],{},[596,3007,604],{},[632,3009,884],{},[587,3011,3012,3014],{},[596,3013,1300],{"stretchy":1361},[632,3015,884],{},[636,3017,3018],{"encoding":638},"\\lambda^2 + 4\\lambda + 4 = (\\lambda + 2)^2",[568,3020,3022,3067,3088,3106,3127],{"className":3021,"ariaHidden":644},[643],[568,3023,3025,3029,3058,3061,3064],{"className":3024},[648],[568,3026],{"className":3027,"style":3028},[652],"height:0.8974em;vertical-align:-0.0833em;",[568,3030,3032,3035],{"className":3031},[657],[568,3033,975],{"className":3034},[657,661],[568,3036,3038],{"className":3037},[666],[568,3039,3041],{"className":3040},[670],[568,3042,3044],{"className":3043},[674],[568,3045,3047],{"className":3046,"style":904},[678],[568,3048,3049,3052],{"style":682},[568,3050],{"className":3051,"style":687},[686],[568,3053,3055],{"className":3054},[691,692,693,694],[568,3056,884],{"className":3057},[657,694],[568,3059],{"className":3060,"style":706},[705],[568,3062,604],{"className":3063},[710],[568,3065],{"className":3066,"style":706},[705],[568,3068,3070,3073,3076,3079,3082,3085],{"className":3069},[648],[568,3071],{"className":3072,"style":1744},[652],[568,3074,889],{"className":3075},[657],[568,3077,975],{"className":3078},[657,661],[568,3080],{"className":3081,"style":706},[705],[568,3083,604],{"className":3084},[710],[568,3086],{"className":3087,"style":706},[705],[568,3089,3091,3094,3097,3100,3103],{"className":3090},[648],[568,3092],{"className":3093,"style":801},[652],[568,3095,889],{"className":3096},[657],[568,3098],{"className":3099,"style":787},[705],[568,3101,630],{"className":3102},[791],[568,3104],{"className":3105,"style":787},[705],[568,3107,3109,3112,3115,3118,3121,3124],{"className":3108},[648],[568,3110],{"className":3111,"style":1764},[652],[568,3113,1281],{"className":3114},[1028],[568,3116,975],{"className":3117},[657,661],[568,3119],{"className":3120,"style":706},[705],[568,3122,604],{"className":3123},[710],[568,3125],{"className":3126,"style":706},[705],[568,3128,3130,3134,3137],{"className":3129},[648],[568,3131],{"className":3132,"style":3133},[652],"height:1.0641em;vertical-align:-0.25em;",[568,3135,884],{"className":3136},[657],[568,3138,3140,3143],{"className":3139},[1103],[568,3141,1300],{"className":3142},[1103],[568,3144,3146],{"className":3145},[666],[568,3147,3149],{"className":3148},[670],[568,3150,3152],{"className":3151},[674],[568,3153,3155],{"className":3154,"style":904},[678],[568,3156,3157,3160],{"style":682},[568,3158],{"className":3159,"style":687},[686],[568,3161,3163],{"className":3162},[691,692,693,694],[568,3164,884],{"className":3165},[657,694],", also ",[568,3168,3170,3190],{"className":3169},[571],[568,3171,3173],{"className":3172},[575],[577,3174,3175],{"xmlns":579},[581,3176,3177,3187],{},[584,3178,3179,3181,3183,3185],{},[590,3180,975],{},[596,3182,630],{},[596,3184,980],{},[632,3186,884],{},[636,3188,3189],{"encoding":638},"\\lambda = -2",[568,3191,3193,3211],{"className":3192,"ariaHidden":644},[643],[568,3194,3196,3199,3202,3205,3208],{"className":3195},[648],[568,3197],{"className":3198,"style":861},[652],[568,3200,975],{"className":3201},[657,661],[568,3203],{"className":3204,"style":787},[705],[568,3206,630],{"className":3207},[791],[568,3209],{"className":3210,"style":787},[705],[568,3212,3214,3218,3221],{"className":3213},[648],[568,3215],{"className":3216,"style":3217},[652],"height:0.7278em;vertical-align:-0.0833em;",[568,3219,980],{"className":3220},[657],[568,3222,884],{"className":3223},[657]," doppelt:",[568,3226,3228],{"className":3227},[1264],[568,3229,3231,3283],{"className":3230},[571],[568,3232,3234],{"className":3233},[575],[577,3235,3236],{"xmlns":579,"display":1273},[581,3237,3238,3280],{},[584,3239,3240,3242,3244,3246,3252,3254,3260,3262,3264,3266,3268],{},[590,3241,592],{},[596,3243,630],{},[596,3245,1281],{"stretchy":1361},[2045,3247,3248,3250],{},[590,3249,2294],{},[632,3251,2297],{},[596,3253,604],{},[2045,3255,3256,3258],{},[590,3257,2294],{},[632,3259,884],{},[609,3261,611],{},[590,3263,1128],{},[596,3265,1300],{"stretchy":1361},[609,3267,611],{},[587,3269,3270,3272],{},[590,3271,1121],{},[584,3273,3274,3276,3278],{},[596,3275,980],{},[632,3277,884],{},[590,3279,1128],{},[636,3281,3282],{"encoding":638},"y = (C_1 + C_2\\,x)\\,e^{-2x}",[568,3284,3286,3304,3362],{"className":3285,"ariaHidden":644},[643],[568,3287,3289,3292,3295,3298,3301],{"className":3288},[648],[568,3290],{"className":3291,"style":2090},[652],[568,3293,592],{"className":3294,"style":662},[657,661],[568,3296],{"className":3297,"style":787},[705],[568,3299,630],{"className":3300},[791],[568,3302],{"className":3303,"style":787},[705],[568,3305,3307,3310,3313,3353,3356,3359],{"className":3306},[648],[568,3308],{"className":3309,"style":1764},[652],[568,3311,1281],{"className":3312},[1028],[568,3314,3316,3319],{"className":3315},[657],[568,3317,2294],{"className":3318,"style":2325},[657,661],[568,3320,3322],{"className":3321},[666],[568,3323,3325,3345],{"className":3324},[670,1036],[568,3326,3328,3342],{"className":3327},[674],[568,3329,3331],{"className":3330,"style":2109},[678],[568,3332,3333,3336],{"style":2340},[568,3334],{"className":3335,"style":687},[686],[568,3337,3339],{"className":3338},[691,692,693,694],[568,3340,2297],{"className":3341},[657,694],[568,3343,1090],{"className":3344},[1089],[568,3346,3348],{"className":3347},[674],[568,3349,3351],{"className":3350,"style":2131},[678],[568,3352],{},[568,3354],{"className":3355,"style":706},[705],[568,3357,604],{"className":3358},[710],[568,3360],{"className":3361,"style":706},[705],[568,3363,3365,3369,3409,3412,3415,3418,3421],{"className":3364},[648],[568,3366],{"className":3367,"style":3368},[652],"height:1.1141em;vertical-align:-0.25em;",[568,3370,3372,3375],{"className":3371},[657],[568,3373,2294],{"className":3374,"style":2325},[657,661],[568,3376,3378],{"className":3377},[666],[568,3379,3381,3401],{"className":3380},[670,1036],[568,3382,3384,3398],{"className":3383},[674],[568,3385,3387],{"className":3386,"style":2109},[678],[568,3388,3389,3392],{"style":2340},[568,3390],{"className":3391,"style":687},[686],[568,3393,3395],{"className":3394},[691,692,693,694],[568,3396,884],{"className":3397},[657,694],[568,3399,1090],{"className":3400},[1089],[568,3402,3404],{"className":3403},[674],[568,3405,3407],{"className":3406,"style":2131},[678],[568,3408],{},[568,3410],{"className":3411,"style":726},[705],[568,3413,1128],{"className":3414},[657,661],[568,3416,1300],{"className":3417},[1103],[568,3419],{"className":3420,"style":726},[705],[568,3422,3424,3427],{"className":3423},[657],[568,3425,1121],{"className":3426},[657,661],[568,3428,3430],{"className":3429},[666],[568,3431,3433],{"className":3432},[670],[568,3434,3436],{"className":3435},[674],[568,3437,3439],{"className":3438,"style":1717},[678],[568,3440,3441,3444],{"style":1456},[568,3442],{"className":3443,"style":687},[686],[568,3445,3447],{"className":3446},[691,692,693,694],[568,3448,3450,3453,3456],{"className":3449},[657,694],[568,3451,980],{"className":3452},[657,694],[568,3454,884],{"className":3455},[657,694],[568,3457,1128],{"className":3458},[657,661,694],[564,3460,3461,3462,2416,3591,3821,3822,3914],{},"Aus 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1",[568,3498,3500,3527,3582],{"className":3499,"ariaHidden":644},[643],[568,3501,3503,3506,3509,3512,3515,3518,3521,3524],{"className":3502},[648],[568,3504],{"className":3505,"style":1764},[652],[568,3507,592],{"className":3508,"style":662},[657,661],[568,3510,1281],{"className":3511},[1028],[568,3513,634],{"className":3514},[657],[568,3516,1300],{"className":3517},[1103],[568,3519],{"className":3520,"style":787},[705],[568,3522,630],{"className":3523},[791],[568,3525],{"className":3526,"style":787},[705],[568,3528,3530,3533,3573,3576,3579],{"className":3529},[648],[568,3531],{"className":3532,"style":2318},[652],[568,3534,3536,3539],{"className":3535},[657],[568,3537,2294],{"className":3538,"style":2325},[657,661],[568,3540,3542],{"className":3541},[666],[568,3543,3545,3565],{"className":3544},[670,1036],[568,3546,3548,3562],{"className":3547},[674],[568,3549,3551],{"className":3550,"style":2109},[678],[568,3552,3553,3556],{"style":2340},[568,3554],{"className":3555,"style":687},[686],[568,3557,3559],{"className":3558},[691,692,693,694],[568,3560,2297],{"className":3561},[657,694],[568,3563,1090],{"className":3564},[1089],[568,3566,3568],{"className":3567},[674],[568,3569,3571],{"className":3570,"style":2131},[678],[568,3572],{},[568,3574],{"className":3575,"style":787},[705],[568,3577,630],{"className":3578},[791],[568,3580],{"className":3581,"style":787},[705],[568,3583,3585,3588],{"className":3584},[648],[568,3586],{"className":3587,"style":801},[652],[568,3589,2297],{"className":3590},[657],[568,3592,3594,3640],{"className":3593},[571],[568,3595,3597],{"className":3596},[575],[577,3598,3599],{"xmlns":579},[581,3600,3601,3637],{},[584,3602,3603,3609,3611,3613,3615,3617,3623,3625,3627,3633,3635],{},[587,3604,3605,3607],{},[590,3606,592],{},[596,3608,599],{"mathvariant":598,"lspace":618,"rspace":618},[596,3610,1281],{"stretchy":1361},[632,3612,634],{},[596,3614,1300],{"stretchy":1361},[596,3616,630],{},[2045,3618,3619,3621],{},[590,3620,2294],{},[632,3622,884],{},[596,3624,980],{},[632,3626,884],{},[2045,3628,3629,3631],{},[590,3630,2294],{},[632,3632,2297],{},[596,3634,630],{},[632,3636,634],{},[636,3638,3639],{"encoding":638},"y'(0) = C_2 - 2C_1 = 0",[568,3641,3643,3699,3754,3812],{"className":3642,"ariaHidden":644},[643],[568,3644,3646,3649,3681,3684,3687,3690,3693,3696],{"className":3645},[648],[568,3647],{"className":3648,"style":2179},[652],[568,3650,3652,3655],{"className":3651},[657],[568,3653,592],{"className":3654,"style":662},[657,661],[568,3656,3658],{"className":3657},[666],[568,3659,3661],{"className":3660},[670],[568,3662,3664],{"className":3663},[674],[568,3665,3667],{"className":3666,"style":679},[678],[568,3668,3669,3672],{"style":682},[568,3670],{"className":3671,"style":687},[686],[568,3673,3675],{"className":3674},[691,692,693,694],[568,3676,3678],{"className":3677},[657,694],[568,3679,599],{"className":3680},[657,694],[568,3682,1281],{"className":3683},[1028],[568,3685,634],{"className":3686},[657],[568,3688,1300],{"className":3689},[1103],[568,3691],{"className":3692,"style":787},[705],[568,3694,630],{"className":3695},[791],[568,3697],{"className":3698,"style":787},[705],[568,3700,3702,3705,3745,3748,3751],{"className":3701},[648],[568,3703],{"className":3704,"style":2318},[652],[568,3706,3708,3711],{"className":3707},[657],[568,3709,2294],{"className":3710,"style":2325},[657,661],[568,3712,3714],{"className":3713},[666],[568,3715,3717,3737],{"className":3716},[670,1036],[568,3718,3720,3734],{"className":3719},[674],[568,3721,3723],{"className":3722,"style":2109},[678],[568,3724,3725,3728],{"style":2340},[568,3726],{"className":3727,"style":687},[686],[568,3729,3731],{"className":3730},[691,692,693,694],[568,3732,884],{"className":3733},[657,694],[568,3735,1090],{"className":3736},[1089],[568,3738,3740],{"className":3739},[674],[568,3741,3743],{"className":3742,"style":2131},[678],[568,3744],{},[568,3746],{"className":3747,"style":706},[705],[568,3749,980],{"className":3750},[710],[568,3752],{"className":3753,"style":706},[705],[568,3755,3757,3760,3763,3803,3806,3809],{"className":3756},[648],[568,3758],{"className":3759,"style":2318},[652],[568,3761,884],{"className":3762},[657],[568,3764,3766,3769],{"className":3765},[657],[568,3767,2294],{"className":3768,"style":2325},[657,661],[568,3770,3772],{"className":3771},[666],[568,3773,3775,3795],{"className":3774},[670,1036],[568,3776,3778,3792],{"className":3777},[674],[568,3779,3781],{"className":3780,"style":2109},[678],[568,3782,3783,3786],{"style":2340},[568,3784],{"className":3785,"style":687},[686],[568,3787,3789],{"className":3788},[691,692,693,694],[568,3790,2297],{"className":3791},[657,694],[568,3793,1090],{"className":3794},[1089],[568,3796,3798],{"className":3797},[674],[568,3799,3801],{"className":3800,"style":2131},[678],[568,3802],{},[568,3804],{"className":3805,"style":787},[705],[568,3807,630],{"className":3808},[791],[568,3810],{"className":3811,"style":787},[705],[568,3813,3815,3818],{"className":3814},[648],[568,3816],{"className":3817,"style":801},[652],[568,3819,634],{"className":3820},[657]," folgt ",[568,3823,3825,3847],{"className":3824},[571],[568,3826,3828],{"className":3827},[575],[577,3829,3830],{"xmlns":579},[581,3831,3832,3844],{},[584,3833,3834,3840,3842],{},[2045,3835,3836,3838],{},[590,3837,2294],{},[632,3839,884],{},[596,3841,630],{},[632,3843,884],{},[636,3845,3846],{"encoding":638},"C_2 = 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= (1 + 2x)\\,e^{-2x}, \\qquad y(1) = 3\\,e^{-2} \\approx 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x}",[568,4250,4252,4270],{"className":4251,"ariaHidden":644},[643],[568,4253,4255,4258,4261,4264,4267],{"className":4254},[648],[568,4256],{"className":4257,"style":2090},[652],[568,4259,592],{"className":4260,"style":662},[657,661],[568,4262],{"className":4263,"style":787},[705],[568,4265,630],{"className":4266},[791],[568,4268],{"className":4269,"style":787},[705],[568,4271,4273,4276,4279,4282],{"className":4272},[648],[568,4274],{"className":4275,"style":1141},[652],[568,4277,2294],{"className":4278,"style":2325},[657,661],[568,4280],{"className":4281,"style":726},[705],[568,4283,4285,4288],{"className":4284},[657],[568,4286,1121],{"className":4287},[657,661],[568,4289,4291],{"className":4290},[666],[568,4292,4294],{"className":4293},[670],[568,4295,4297],{"className":4296},[674],[568,4298,4300],{"className":4299,"style":1141},[678],[568,4301,4302,4305],{"style":682},[568,4303],{"className":4304,"style":687},[686],[568,4306,4308],{"className":4307},[691,692,693,694],[568,4309,4311,4314],{"className":4310},[657,694],[568,4312,975],{"className":4313},[657,661,694],[568,4315,1128],{"className":4316},[657,661,694]," angeben. Damit lassen sich zwei Anfangswerte im Allgemeinen nicht erfüllen.",[4213,4319,4320,4554,4555,4749],{},[568,4321,4323,4373],{"className":4322},[571],[568,4324,4326],{"className":4325},[575],[577,4327,4328],{"xmlns":579},[581,4329,4330,4370],{},[584,4331,4332,4338,4340,4350,4352,4358,4360],{},[2045,4333,4334,4336],{},[590,4335,2294],{},[632,4337,2297],{},[609,4339,611],{},[587,4341,4342,4344],{},[590,4343,1121],{},[584,4345,4346,4348],{},[590,4347,975],{},[590,4349,1128],{},[596,4351,604],{},[2045,4353,4354,4356],{},[590,4355,2294],{},[632,4357,884],{},[609,4359,611],{},[587,4361,4362,4364],{},[590,4363,1121],{},[584,4365,4366,4368],{},[590,4367,975],{},[590,4369,1128],{},[636,4371,4372],{"encoding":638},"C_1\\,e^{\\lambda x} + C_2\\,e^{\\lambda x}",[568,4374,4376,4470],{"className":4375,"ariaHidden":644},[643],[568,4377,4379,4383,4423,4426,4461,4464,4467],{"className":4378},[648],[568,4380],{"className":4381,"style":4382},[652],"height:0.9991em;vertical-align:-0.15em;",[568,4384,4386,4389],{"className":4385},[657],[568,4387,2294],{"className":4388,"style":2325},[657,661],[568,4390,4392],{"className":4391},[666],[568,4393,4395,4415],{"className":4394},[670,1036],[568,4396,4398,4412],{"className":4397},[674],[568,4399,4401],{"className":4400,"style":2109},[678],[568,4402,4403,4406],{"style":2340},[568,4404],{"className":4405,"style":687},[686],[568,4407,4409],{"className":4408},[691,692,693,694],[568,4410,2297],{"className":4411},[657,694],[568,4413,1090],{"className":4414},[1089],[568,4416,4418],{"className":4417},[674],[568,4419,4421],{"className":4420,"style":2131},[678],[568,4422],{},[568,4424],{"className":4425,"style":726},[705],[568,4427,4429,4432],{"className":4428},[657],[568,4430,1121],{"className":4431},[657,661],[568,4433,4435],{"className":4434},[666],[568,4436,4438],{"className":4437},[670],[568,4439,4441],{"className":4440},[674],[568,4442,4444],{"className":4443,"style":1141},[678],[568,4445,4446,4449],{"style":682},[568,4447],{"className":4448,"style":687},[686],[568,4450,4452],{"className":4451},[691,692,693,694],[568,4453,4455,4458],{"className":4454},[657,694],[568,4456,975],{"className":4457},[657,661,694],[568,4459,1128],{"className":4460},[657,661,694],[568,4462],{"className":4463,"style":706},[705],[568,4465,604],{"className":4466},[710],[568,4468],{"className":4469,"style":706},[705],[568,4471,4473,4476,4516,4519],{"className":4472},[648],[568,4474],{"className":4475,"style":4382},[652],[568,4477,4479,4482],{"className":4478},[657],[568,4480,2294],{"className":4481,"style":2325},[657,661],[568,4483,4485],{"className":4484},[666],[568,4486,4488,4508],{"className":4487},[670,1036],[568,4489,4491,4505],{"className":4490},[674],[568,4492,4494],{"className":4493,"style":2109},[678],[568,4495,4496,4499],{"style":2340},[568,4497],{"className":4498,"style":687},[686],[568,4500,4502],{"className":4501},[691,692,693,694],[568,4503,884],{"className":4504},[657,694],[568,4506,1090],{"className":4507},[1089],[568,4509,4511],{"className":4510},[674],[568,4512,4514],{"className":4513,"style":2131},[678],[568,4515],{},[568,4517],{"className":4518,"style":726},[705],[568,4520,4522,4525],{"className":4521},[657],[568,4523,1121],{"className":4524},[657,661],[568,4526,4528],{"className":4527},[666],[568,4529,4531],{"className":4530},[670],[568,4532,4534],{"className":4533},[674],[568,4535,4537],{"className":4536,"style":1141},[678],[568,4538,4539,4542],{"style":682},[568,4540],{"className":4541,"style":687},[686],[568,4543,4545],{"className":4544},[691,692,693,694],[568,4546,4548,4551],{"className":4547},[657,694],[568,4549,975],{"className":4550},[657,661,694],[568,4552,1128],{"className":4553},[657,661,694]," schreiben. Das ist ",[568,4556,4558,4600],{"className":4557},[571],[568,4559,4561],{"className":4560},[575],[577,4562,4563],{"xmlns":579},[581,4564,4565,4597],{},[584,4566,4567,4569,4575,4577,4583,4585,4587],{},[596,4568,1281],{"stretchy":1361},[2045,4570,4571,4573],{},[590,4572,2294],{},[632,4574,2297],{},[596,4576,604],{},[2045,4578,4579,4581],{},[590,4580,2294],{},[632,4582,884],{},[596,4584,1300],{"stretchy":1361},[609,4586,611],{},[587,4588,4589,4591],{},[590,4590,1121],{},[584,4592,4593,4595],{},[590,4594,975],{},[590,4596,1128],{},[636,4598,4599],{"encoding":638},"(C_1 + C_2)\\,e^{\\lambda x}",[568,4601,4603,4661],{"className":4602,"ariaHidden":644},[643],[568,4604,4606,4609,4612,4652,4655,4658],{"className":4605},[648],[568,4607],{"className":4608,"style":1764},[652],[568,4610,1281],{"className":4611},[1028],[568,4613,4615,4618],{"className":4614},[657],[568,4616,2294],{"className":4617,"style":2325},[657,661],[568,4619,4621],{"className":4620},[666],[568,4622,4624,4644],{"className":4623},[670,1036],[568,4625,4627,4641],{"className":4626},[674],[568,4628,4630],{"className":4629,"style":2109},[678],[568,4631,4632,4635],{"style":2340},[568,4633],{"className":4634,"style":687},[686],[568,4636,4638],{"className":4637},[691,692,693,694],[568,4639,2297],{"className":4640},[657,694],[568,4642,1090],{"className":4643},[1089],[568,4645,4647],{"className":4646},[674],[568,4648,4650],{"className":4649,"style":2131},[678],[568,4651],{},[568,4653],{"className":4654,"style":706},[705],[568,4656,604],{"className":4657},[710],[568,4659],{"className":4660,"style":706},[705],[568,4662,4664,4668,4708,4711,4714],{"className":4663},[648],[568,4665],{"className":4666,"style":4667},[652],"height:1.0991em;vertical-align:-0.25em;",[568,4669,4671,4674],{"className":4670},[657],[568,4672,2294],{"className":4673,"style":2325},[657,661],[568,4675,4677],{"className":4676},[666],[568,4678,4680,4700],{"className":4679},[670,1036],[568,4681,4683,4697],{"className":4682},[674],[568,4684,4686],{"className":4685,"style":2109},[678],[568,4687,4688,4691],{"style":2340},[568,4689],{"className":4690,"style":687},[686],[568,4692,4694],{"className":4693},[691,692,693,694],[568,4695,884],{"className":4696},[657,694],[568,4698,1090],{"className":4699},[1089],[568,4701,4703],{"className":4702},[674],[568,4704,4706],{"className":4705,"style":2131},[678],[568,4707],{},[568,4709,1300],{"className":4710},[1103],[568,4712],{"className":4713,"style":726},[705],[568,4715,4717,4720],{"className":4716},[657],[568,4718,1121],{"className":4719},[657,661],[568,4721,4723],{"className":4722},[666],[568,4724,4726],{"className":4725},[670],[568,4727,4729],{"className":4728},[674],[568,4730,4732],{"className":4731,"style":1141},[678],[568,4733,4734,4737],{"style":682},[568,4735],{"className":4736,"style":687},[686],[568,4738,4740],{"className":4739},[691,692,693,694],[568,4741,4743,4746],{"className":4742},[657,694],[568,4744,975],{"className":4745},[657,661,694],[568,4747,1128],{"className":4748},[657,661,694],", also nur eine Lösung.",[4213,4751,4752,4753,4830,4831,4909,4910,5026,5027,5055,5056,5084],{},"Bei ",[568,4754,4756,4780],{"className":4755},[571],[568,4757,4759],{"className":4758},[575],[577,4760,4761],{"xmlns":579},[581,4762,4763,4777],{},[584,4764,4765,4771,4773,4775],{},[587,4766,4767,4769],{},[590,4768,592],{},[596,4770,599],{"mathvariant":598,"lspace":618,"rspace":618},[596,4772,1281],{"stretchy":1361},[632,4774,634],{},[596,4776,1300],{"stretchy":1361},[636,4778,4779],{"encoding":638},"y'(0)",[568,4781,4783],{"className":4782,"ariaHidden":644},[643],[568,4784,4786,4789,4821,4824,4827],{"className":4785},[648],[568,4787],{"className":4788,"style":2179},[652],[568,4790,4792,4795],{"className":4791},[657],[568,4793,592],{"className":4794,"style":662},[657,661],[568,4796,4798],{"className":4797},[666],[568,4799,4801],{"className":4800},[670],[568,4802,4804],{"className":4803},[674],[568,4805,4807],{"className":4806,"style":679},[678],[568,4808,4809,4812],{"style":682},[568,4810],{"className":4811,"style":687},[686],[568,4813,4815],{"className":4814},[691,692,693,694],[568,4816,4818],{"className":4817},[657,694],[568,4819,599],{"className":4820},[657,694],[568,4822,1281],{"className":4823},[1028],[568,4825,634],{"className":4826},[657],[568,4828,1300],{"className":4829},[1103]," die Produktregel vergessen: Die Ableitung von ",[568,4832,4834,4859],{"className":4833},[571],[568,4835,4837],{"className":4836},[575],[577,4838,4839],{"xmlns":579},[581,4840,4841,4857],{},[584,4842,4843,4845,4847],{},[590,4844,1128],{},[609,4846,611],{},[587,4848,4849,4851],{},[590,4850,1121],{},[584,4852,4853,4855],{},[590,4854,975],{},[590,4856,1128],{},[636,4858,1209],{"encoding":638},[568,4860,4862],{"className":4861,"ariaHidden":644},[643],[568,4863,4865,4868,4871,4874],{"className":4864},[648],[568,4866],{"className":4867,"style":1141},[652],[568,4869,1128],{"className":4870},[657,661],[568,4872],{"className":4873,"style":726},[705],[568,4875,4877,4880],{"className":4876},[657],[568,4878,1121],{"className":4879},[657,661],[568,4881,4883],{"className":4882},[666],[568,4884,4886],{"className":4885},[670],[568,4887,4889],{"className":4888},[674],[568,4890,4892],{"className":4891,"style":1141},[678],[568,4893,4894,4897],{"style":682},[568,4895],{"className":4896,"style":687},[686],[568,4898,4900],{"className":4899},[691,692,693,694],[568,4901,4903,4906],{"className":4902},[657,694],[568,4904,975],{"className":4905},[657,661,694],[568,4907,1128],{"className":4908},[657,661,694]," ist ",[568,4911,4913,4949],{"className":4912},[571],[568,4914,4916],{"className":4915},[575],[577,4917,4918],{"xmlns":579},[581,4919,4920,4946],{},[584,4921,4922,4924,4926,4928,4930,4932,4934,4936],{},[596,4923,1281],{"stretchy":1361},[632,4925,2297],{},[596,4927,604],{},[590,4929,975],{},[590,4931,1128],{},[596,4933,1300],{"stretchy":1361},[609,4935,611],{},[587,4937,4938,4940],{},[590,4939,1121],{},[584,4941,4942,4944],{},[590,4943,975],{},[590,4945,1128],{},[636,4947,4948],{"encoding":638},"(1 + \\lambda x)\\,e^{\\lambda x}",[568,4950,4952,4973],{"className":4951,"ariaHidden":644},[643],[568,4953,4955,4958,4961,4964,4967,4970],{"className":4954},[648],[568,4956],{"className":4957,"style":1764},[652],[568,4959,1281],{"className":4960},[1028],[568,4962,2297],{"className":4963},[657],[568,4965],{"className":4966,"style":706},[705],[568,4968,604],{"className":4969},[710],[568,4971],{"className":4972,"style":706},[705],[568,4974,4976,4979,4982,4985,4988,4991],{"className":4975},[648],[568,4977],{"className":4978,"style":4667},[652],[568,4980,975],{"className":4981},[657,661],[568,4983,1128],{"className":4984},[657,661],[568,4986,1300],{"className":4987},[1103],[568,4989],{"className":4990,"style":726},[705],[568,4992,4994,4997],{"className":4993},[657],[568,4995,1121],{"className":4996},[657,661],[568,4998,5000],{"className":4999},[666],[568,5001,5003],{"className":5002},[670],[568,5004,5006],{"className":5005},[674],[568,5007,5009],{"className":5008,"style":1141},[678],[568,5010,5011,5014],{"style":682},[568,5012],{"className":5013,"style":687},[686],[568,5015,5017],{"className":5016},[691,692,693,694],[568,5018,5020,5023],{"className":5019},[657,694],[568,5021,975],{"className":5022},[657,661,694],[568,5024,1128],{"className":5025},[657,661,694],", an der Stelle ",[568,5028,5030,5043],{"className":5029},[571],[568,5031,5033],{"className":5032},[575],[577,5034,5035],{"xmlns":579},[581,5036,5037,5041],{},[584,5038,5039],{},[632,5040,634],{},[636,5042,634],{"encoding":638},[568,5044,5046],{"className":5045,"ariaHidden":644},[643],[568,5047,5049,5052],{"className":5048},[648],[568,5050],{"className":5051,"style":801},[652],[568,5053,634],{"className":5054},[657]," also ",[568,5057,5059,5072],{"className":5058},[571],[568,5060,5062],{"className":5061},[575],[577,5063,5064],{"xmlns":579},[581,5065,5066,5070],{},[584,5067,5068],{},[632,5069,2297],{},[636,5071,2297],{"encoding":638},[568,5073,5075],{"className":5074,"ariaHidden":644},[643],[568,5076,5078,5081],{"className":5077},[648],[568,5079],{"className":5080,"style":801},[652],[568,5082,2297],{"className":5083},[657],".",[4213,5086,5087,5088,5116,5117,5221,5222,5084],{},"Den Faktor ",[568,5089,5091,5104],{"className":5090},[571],[568,5092,5094],{"className":5093},[575],[577,5095,5096],{"xmlns":579},[581,5097,5098,5102],{},[584,5099,5100],{},[590,5101,1128],{},[636,5103,1128],{"encoding":638},[568,5105,5107],{"className":5106,"ariaHidden":644},[643],[568,5108,5110,5113],{"className":5109},[648],[568,5111],{"className":5112,"style":831},[652],[568,5114,1128],{"className":5115},[657,661]," an die falsche Stelle setzen, z.B. ",[568,5118,5120,5146],{"className":5119},[571],[568,5121,5123],{"className":5122},[575],[577,5124,5125],{"xmlns":579},[581,5126,5127,5143],{},[584,5128,5129],{},[587,5130,5131,5133],{},[590,5132,1121],{},[584,5134,5135,5137],{},[590,5136,975],{},[587,5138,5139,5141],{},[590,5140,1128],{},[632,5142,884],{},[636,5144,5145],{"encoding":638},"e^{\\lambda x^2}",[568,5147,5149],{"className":5148,"ariaHidden":644},[643],[568,5150,5152,5156],{"className":5151},[648],[568,5153],{"className":5154,"style":5155},[652],"height:0.9869em;",[568,5157,5159,5162],{"className":5158},[657],[568,5160,1121],{"className":5161},[657,661],[568,5163,5165],{"className":5164},[666],[568,5166,5168],{"className":5167},[670],[568,5169,5171],{"className":5170},[674],[568,5172,5174],{"className":5173,"style":5155},[678],[568,5175,5176,5179],{"style":682},[568,5177],{"className":5178,"style":687},[686],[568,5180,5182],{"className":5181},[691,692,693,694],[568,5183,5185,5188],{"className":5184},[657,694],[568,5186,975],{"className":5187},[657,661,694],[568,5189,5191,5194],{"className":5190},[657,694],[568,5192,1128],{"className":5193},[657,661,694],[568,5195,5197],{"className":5196},[666],[568,5198,5200],{"className":5199},[670],[568,5201,5203],{"className":5202},[674],[568,5204,5207],{"className":5205,"style":5206},[678],"height:0.8913em;",[568,5208,5210,5214],{"style":5209},"top:-2.931em;margin-right:0.0714em;",[568,5211],{"className":5212,"style":5213},[686],"height:2.5em;",[568,5215,5218],{"className":5216},[691,5217,1428,694],"reset-size3",[568,5219,884],{"className":5220},[657,694]," statt 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