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Dann sind ",[567,1279,1281,1309],{"className":1280},[570],[567,1282,1284],{"className":1283},[574],[576,1285,1286],{"xmlns":578},[580,1287,1288,1306],{},[583,1289,1290],{},[586,1291,1292,1295],{},[589,1293,1294],{},"e",[583,1296,1297,1303],{},[1107,1298,1299,1301],{},[589,1300,973],{},[631,1302,1113],{},[589,1304,1305],{},"x",[635,1307,1308],{"encoding":637},"e^{\\lambda_1 x}",[567,1310,1312],{"className":1311,"ariaHidden":643},[642],[567,1313,1315,1319],{"className":1314},[647],[567,1316],{"className":1317,"style":1318},[651],"height:0.8491em;",[567,1320,1322,1325],{"className":1321},[656],[567,1323,1294],{"className":1324},[656,660],[567,1326,1328],{"className":1327},[665],[567,1329,1331],{"className":1330},[669],[567,1332,1334],{"className":1333},[673],[567,1335,1337],{"className":1336,"style":1318},[677],[567,1338,1339,1342],{"style":681},[567,1340],{"className":1341,"style":686},[685],[567,1343,1345],{"className":1344},[690,691,692,693],[567,1346,1348,1394],{"className":1347},[656,693],[567,1349,1351,1354],{"className":1350},[656,693],[567,1352,973],{"className":1353},[656,660,693],[567,1355,1357],{"className":1356},[665],[567,1358,1360,1385],{"className":1359},[669,1147],[567,1361,1363,1382],{"className":1362},[673],[567,1364,1367],{"className":1365,"style":1366},[677],"height:0.3173em;",[567,1368,1370,1374],{"style":1369},"top:-2.357em;margin-left:0em;margin-right:0.0714em;",[567,1371],{"className":1372,"style":1373},[685],"height:2.5em;",[567,1375,1379],{"className":1376},[690,1377,1378,693],"reset-size3","size1",[567,1380,1113],{"className":1381},[656,693],[567,1383,1171],{"className":1384},[1170],[567,1386,1388],{"className":1387},[673],[567,1389,1392],{"className":1390,"style":1391},[677],"height:0.143em;",[567,1393],{},[567,1395,1305],{"className":1396},[656,660,693]," und ",[567,1399,1401,1427],{"className":1400},[570],[567,1402,1404],{"className":1403},[574],[576,1405,1406],{"xmlns":578},[580,1407,1408,1424],{},[583,1409,1410],{},[586,1411,1412,1414],{},[589,1413,1294],{},[583,1415,1416,1422],{},[1107,1417,1418,1420],{},[589,1419,973],{},[631,1421,883],{},[589,1423,1305],{},[635,1425,1426],{"encoding":637},"e^{\\lambda_2 x}",[567,1428,1430],{"className":1429,"ariaHidden":643},[642],[567,1431,1433,1436],{"className":1432},[647],[567,1434],{"className":1435,"style":1318},[651],[567,1437,1439,1442],{"className":1438},[656],[567,1440,1294],{"className":1441},[656,660],[567,1443,1445],{"className":1444},[665],[567,1446,1448],{"className":1447},[669],[567,1449,1451],{"className":1450},[673],[567,1452,1454],{"className":1453,"style":1318},[677],[567,1455,1456,1459],{"style":681},[567,1457],{"className":1458,"style":686},[685],[567,1460,1462],{"className":1461},[690,691,692,693],[567,1463,1465,1505],{"className":1464},[656,693],[567,1466,1468,1471],{"className":1467},[656,693],[567,1469,973],{"className":1470},[656,660,693],[567,1472,1474],{"className":1473},[665],[567,1475,1477,1497],{"className":1476},[669,1147],[567,1478,1480,1494],{"className":1479},[673],[567,1481,1483],{"className":1482,"style":1366},[677],[567,1484,1485,1488],{"style":1369},[567,1486],{"className":1487,"style":1373},[685],[567,1489,1491],{"className":1490},[690,1377,1378,693],[567,1492,883],{"className":1493},[656,693],[567,1495,1171],{"className":1496},[1170],[567,1498,1500],{"className":1499},[673],[567,1501,1503],{"className":1502,"style":1391},[677],[567,1504],{},[567,1506,1305],{"className":1507},[656,660,693]," zwei linear unabhängige Lösungen, und jede Lösung ist eine Linearkombination davon.",[563,1510,1511,1512,834,1586,1656,1657,1397,1772,1915],{},"Die Konstanten ",[567,1513,1515,1534],{"className":1514},[570],[567,1516,1518],{"className":1517},[574],[576,1519,1520],{"xmlns":578},[580,1521,1522,1531],{},[583,1523,1524],{},[1107,1525,1526,1529],{},[589,1527,1528],{},"C",[631,1530,1113],{},[635,1532,1533],{"encoding":637},"C_1",[567,1535,1537],{"className":1536,"ariaHidden":643},[642],[567,1538,1540,1544],{"className":1539},[647],[567,1541],{"className":1542,"style":1543},[651],"height:0.8333em;vertical-align:-0.15em;",[567,1545,1547,1551],{"className":1546},[656],[567,1548,1528],{"className":1549,"style":1550},[656,660],"margin-right:0.0715em;",[567,1552,1554],{"className":1553},[665],[567,1555,1557,1578],{"className":1556},[669,1147],[567,1558,1560,1575],{"className":1559},[673],[567,1561,1563],{"className":1562,"style":1154},[677],[567,1564,1566,1569],{"style":1565},"top:-2.55em;margin-left:-0.0715em;margin-right:0.05em;",[567,1567],{"className":1568,"style":686},[685],[567,1570,1572],{"className":1571},[690,691,692,693],[567,1573,1113],{"className":1574},[656,693],[567,1576,1171],{"className":1577},[1170],[567,1579,1581],{"className":1580},[673],[567,1582,1584],{"className":1583,"style":1178},[677],[567,1585],{},[567,1587,1589,1607],{"className":1588},[570],[567,1590,1592],{"className":1591},[574],[576,1593,1594],{"xmlns":578},[580,1595,1596,1604],{},[583,1597,1598],{},[1107,1599,1600,1602],{},[589,1601,1528],{},[631,1603,883],{},[635,1605,1606],{"encoding":637},"C_2",[567,1608,1610],{"className":1609,"ariaHidden":643},[642],[567,1611,1613,1616],{"className":1612},[647],[567,1614],{"className":1615,"style":1543},[651],[567,1617,1619,1622],{"className":1618},[656],[567,1620,1528],{"className":1621,"style":1550},[656,660],[567,1623,1625],{"className":1624},[665],[567,1626,1628,1648],{"className":1627},[669,1147],[567,1629,1631,1645],{"className":1630},[673],[567,1632,1634],{"className":1633,"style":1154},[677],[567,1635,1636,1639],{"style":1565},[567,1637],{"className":1638,"style":686},[685],[567,1640,1642],{"className":1641},[690,691,692,693],[567,1643,883],{"className":1644},[656,693],[567,1646,1171],{"className":1647},[1170],[567,1649,1651],{"className":1650},[673],[567,1652,1654],{"className":1653,"style":1178},[677],[567,1655],{}," legt man über zwei Bedingungen fest, meist ",[567,1658,1660,1691],{"className":1659},[570],[567,1661,1663],{"className":1662},[574],[576,1664,1665],{"xmlns":578},[580,1666,1667,1688],{},[583,1668,1669,1671,1675,1677,1680,1682],{},[589,1670,591],{},[595,1672,1674],{"stretchy":1673},"false","(",[631,1676,633],{},[595,1678,1679],{"stretchy":1673},")",[595,1681,629],{},[1107,1683,1684,1686],{},[589,1685,591],{},[631,1687,633],{},[635,1689,1690],{"encoding":637},"y(0) = y_0",[567,1692,1694,1724],{"className":1693,"ariaHidden":643},[642],[567,1695,1697,1701,1704,1708,1711,1715,1718,1721],{"className":1696},[647],[567,1698],{"className":1699,"style":1700},[651],"height:1em;vertical-align:-0.25em;",[567,1702,591],{"className":1703,"style":661},[656,660],[567,1705,1674],{"className":1706},[1707],"mopen",[567,1709,633],{"className":1710},[656],[567,1712,1679],{"className":1713},[1714],"mclose",[567,1716],{"className":1717,"style":786},[704],[567,1719,629],{"className":1720},[790],[567,1722],{"className":1723,"style":786},[704],[567,1725,1727,1731],{"className":1726},[647],[567,1728],{"className":1729,"style":1730},[651],"height:0.625em;vertical-align:-0.1944em;",[567,1732,1734,1737],{"className":1733},[656],[567,1735,591],{"className":1736,"style":661},[656,660],[567,1738,1740],{"className":1739},[665],[567,1741,1743,1764],{"className":1742},[669,1147],[567,1744,1746,1761],{"className":1745},[673],[567,1747,1749],{"className":1748,"style":1154},[677],[567,1750,1752,1755],{"style":1751},"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;",[567,1753],{"className":1754,"style":686},[685],[567,1756,1758],{"className":1757},[690,691,692,693],[567,1759,633],{"className":1760},[656,693],[567,1762,1171],{"className":1763},[1170],[567,1765,1767],{"className":1766},[673],[567,1768,1770],{"className":1769,"style":1178},[677],[567,1771],{},[567,1773,1775,1808],{"className":1774},[570],[567,1776,1778],{"className":1777},[574],[576,1779,1780],{"xmlns":578},[580,1781,1782,1805],{},[583,1783,1784,1790,1792,1794,1796,1798],{},[586,1785,1786,1788],{},[589,1787,591],{},[595,1789,598],{"mathvariant":597,"lspace":617,"rspace":617},[595,1791,1674],{"stretchy":1673},[631,1793,633],{},[595,1795,1679],{"stretchy":1673},[595,1797,629],{},[1107,1799,1800,1803],{},[589,1801,1802],{},"v",[631,1804,633],{},[635,1806,1807],{"encoding":637},"y'(0) = v_0",[567,1809,1811,1868],{"className":1810,"ariaHidden":643},[642],[567,1812,1814,1818,1850,1853,1856,1859,1862,1865],{"className":1813},[647],[567,1815],{"className":1816,"style":1817},[651],"height:1.0019em;vertical-align:-0.25em;",[567,1819,1821,1824],{"className":1820},[656],[567,1822,591],{"className":1823,"style":661},[656,660],[567,1825,1827],{"className":1826},[665],[567,1828,1830],{"className":1829},[669],[567,1831,1833],{"className":1832},[673],[567,1834,1836],{"className":1835,"style":678},[677],[567,1837,1838,1841],{"style":681},[567,1839],{"className":1840,"style":686},[685],[567,1842,1844],{"className":1843},[690,691,692,693],[567,1845,1847],{"className":1846},[656,693],[567,1848,598],{"className":1849},[656,693],[567,1851,1674],{"className":1852},[1707],[567,1854,633],{"className":1855},[656],[567,1857,1679],{"className":1858},[1714],[567,1860],{"className":1861,"style":786},[704],[567,1863,629],{"className":1864},[790],[567,1866],{"className":1867,"style":786},[704],[567,1869,1871,1875],{"className":1870},[647],[567,1872],{"className":1873,"style":1874},[651],"height:0.5806em;vertical-align:-0.15em;",[567,1876,1878,1881],{"className":1877},[656],[567,1879,1802],{"className":1880,"style":661},[656,660],[567,1882,1884],{"className":1883},[665],[567,1885,1887,1907],{"className":1886},[669,1147],[567,1888,1890,1904],{"className":1889},[673],[567,1891,1893],{"className":1892,"style":1154},[677],[567,1894,1895,1898],{"style":1751},[567,1896],{"className":1897,"style":686},[685],[567,1899,1901],{"className":1900},[690,691,692,693],[567,1902,633],{"className":1903},[656,693],[567,1905,1171],{"className":1906},[1170],[567,1908,1910],{"className":1909},[673],[567,1911,1913],{"className":1912,"style":1178},[677],[567,1914],{},". Das ergibt das lineare Gleichungssystem",[567,1917,1920],{"className":1918},[1919],"katex-display",[567,1921,1923,1998],{"className":1922},[570],[567,1924,1926],{"className":1925},[574],[576,1927,1929],{"xmlns":578,"display":1928},"block",[580,1930,1931,1995],{},[583,1932,1933,1939,1941,1947,1949,1955,1958,1961,1967,1973,1975,1981,1987,1989],{},[1107,1934,1935,1937],{},[589,1936,1528],{},[631,1938,1113],{},[595,1940,603],{},[1107,1942,1943,1945],{},[589,1944,1528],{},[631,1946,883],{},[595,1948,629],{},[1107,1950,1951,1953],{},[589,1952,591],{},[631,1954,633],{},[595,1956,1957],{"separator":643},",",[704,1959],{"width":1960},"2em",[1107,1962,1963,1965],{},[589,1964,973],{},[631,1966,1113],{},[1107,1968,1969,1971],{},[589,1970,1528],{},[631,1972,1113],{},[595,1974,603],{},[1107,1976,1977,1979],{},[589,1978,973],{},[631,1980,883],{},[1107,1982,1983,1985],{},[589,1984,1528],{},[631,1986,883],{},[595,1988,629],{},[1107,1990,1991,1993],{},[589,1992,1802],{},[631,1994,633],{},[635,1996,1997],{"encoding":637},"C_1 + C_2 = y_0, \\qquad \\lambda_1 C_1 + \\lambda_2 C_2 = v_0",[567,1999,2001,2056,2111,2257,2352],{"className":2000,"ariaHidden":643},[642],[567,2002,2004,2007,2047,2050,2053],{"className":2003},[647],[567,2005],{"className":2006,"style":1543},[651],[567,2008,2010,2013],{"className":2009},[656],[567,2011,1528],{"className":2012,"style":1550},[656,660],[567,2014,2016],{"className":2015},[665],[567,2017,2019,2039],{"className":2018},[669,1147],[567,2020,2022,2036],{"className":2021},[673],[567,2023,2025],{"className":2024,"style":1154},[677],[567,2026,2027,2030],{"style":1565},[567,2028],{"className":2029,"style":686},[685],[567,2031,2033],{"className":2032},[690,691,692,693],[567,2034,1113],{"className":2035},[656,693],[567,2037,1171],{"className":2038},[1170],[567,2040,2042],{"className":2041},[673],[567,2043,2045],{"className":2044,"style":1178},[677],[567,2046],{},[567,2048],{"className":2049,"style":705},[704],[567,2051,603],{"className":2052},[709],[567,2054],{"className":2055,"style":705},[704],[567,2057,2059,2062,2102,2105,2108],{"className":2058},[647],[567,2060],{"className":2061,"style":1543},[651],[567,2063,2065,2068],{"className":2064},[656],[567,2066,1528],{"className":2067,"style":1550},[656,660],[567,2069,2071],{"className":2070},[665],[567,2072,2074,2094],{"className":2073},[669,1147],[567,2075,2077,2091],{"className":2076},[673],[567,2078,2080],{"className":2079,"style":1154},[677],[567,2081,2082,2085],{"style":1565},[567,2083],{"className":2084,"style":686},[685],[567,2086,2088],{"className":2087},[690,691,692,693],[567,2089,883],{"className":2090},[656,693],[567,2092,1171],{"className":2093},[1170],[567,2095,2097],{"className":2096},[673],[567,2098,2100],{"className":2099,"style":1178},[677],[567,2101],{},[567,2103],{"className":2104,"style":786},[704],[567,2106,629],{"className":2107},[790],[567,2109],{"className":2110,"style":786},[704],[567,2112,2114,2117,2157,2161,2165,2168,2208,2248,2251,2254],{"className":2113},[647],[567,2115],{"className":2116,"style":773},[651],[567,2118,2120,2123],{"className":2119},[656],[567,2121,591],{"className":2122,"style":661},[656,660],[567,2124,2126],{"className":2125},[665],[567,2127,2129,2149],{"className":2128},[669,1147],[567,2130,2132,2146],{"className":2131},[673],[567,2133,2135],{"className":2134,"style":1154},[677],[567,2136,2137,2140],{"style":1751},[567,2138],{"className":2139,"style":686},[685],[567,2141,2143],{"className":2142},[690,691,692,693],[567,2144,633],{"className":2145},[656,693],[567,2147,1171],{"className":2148},[1170],[567,2150,2152],{"className":2151},[673],[567,2153,2155],{"className":2154,"style":1178},[677],[567,2156],{},[567,2158,1957],{"className":2159},[2160],"mpunct",[567,2162],{"className":2163,"style":2164},[704],"margin-right:2em;",[567,2166],{"className":2167,"style":725},[704],[567,2169,2171,2174],{"className":2170},[656],[567,2172,973],{"className":2173},[656,660],[567,2175,2177],{"className":2176},[665],[567,2178,2180,2200],{"className":2179},[669,1147],[567,2181,2183,2197],{"className":2182},[673],[567,2184,2186],{"className":2185,"style":1154},[677],[567,2187,2188,2191],{"style":1157},[567,2189],{"className":2190,"style":686},[685],[567,2192,2194],{"className":2193},[690,691,692,693],[567,2195,1113],{"className":2196},[656,693],[567,2198,1171],{"className":2199},[1170],[567,2201,2203],{"className":2202},[673],[567,2204,2206],{"className":2205,"style":1178},[677],[567,2207],{},[567,2209,2211,2214],{"className":2210},[656],[567,2212,1528],{"className":2213,"style":1550},[656,660],[567,2215,2217],{"className":2216},[665],[567,2218,2220,2240],{"className":2219},[669,1147],[567,2221,2223,2237],{"className":2222},[673],[567,2224,2226],{"className":2225,"style":1154},[677],[567,2227,2228,2231],{"style":1565},[567,2229],{"className":2230,"style":686},[685],[567,2232,2234],{"className":2233},[690,691,692,693],[567,2235,1113],{"className":2236},[656,693],[567,2238,1171],{"className":2239},[1170],[567,2241,2243],{"className":2242},[673],[567,2244,2246],{"className":2245,"style":1178},[677],[567,2247],{},[567,2249],{"className":2250,"style":705},[704],[567,2252,603],{"className":2253},[709],[567,2255],{"className":2256,"style":705},[704],[567,2258,2260,2263,2303,2343,2346,2349],{"className":2259},[647],[567,2261],{"className":2262,"style":1236},[651],[567,2264,2266,2269],{"className":2265},[656],[567,2267,973],{"className":2268},[656,660],[567,2270,2272],{"className":2271},[665],[567,2273,2275,2295],{"className":2274},[669,1147],[567,2276,2278,2292],{"className":2277},[673],[567,2279,2281],{"className":2280,"style":1154},[677],[567,2282,2283,2286],{"style":1157},[567,2284],{"className":2285,"style":686},[685],[567,2287,2289],{"className":2288},[690,691,692,693],[567,2290,883],{"className":2291},[656,693],[567,2293,1171],{"className":2294},[1170],[567,2296,2298],{"className":2297},[673],[567,2299,2301],{"className":2300,"style":1178},[677],[567,2302],{},[567,2304,2306,2309],{"className":2305},[656],[567,2307,1528],{"className":2308,"style":1550},[656,660],[567,2310,2312],{"className":2311},[665],[567,2313,2315,2335],{"className":2314},[669,1147],[567,2316,2318,2332],{"className":2317},[673],[567,2319,2321],{"className":2320,"style":1154},[677],[567,2322,2323,2326],{"style":1565},[567,2324],{"className":2325,"style":686},[685],[567,2327,2329],{"className":2328},[690,691,692,693],[567,2330,883],{"className":2331},[656,693],[567,2333,1171],{"className":2334},[1170],[567,2336,2338],{"className":2337},[673],[567,2339,2341],{"className":2340,"style":1178},[677],[567,2342],{},[567,2344],{"className":2345,"style":786},[704],[567,2347,629],{"className":2348},[790],[567,2350],{"className":2351,"style":786},[704],[567,2353,2355,2358],{"className":2354},[647],[567,2356],{"className":2357,"style":1874},[651],[567,2359,2361,2364],{"className":2360},[656],[567,2362,1802],{"className":2363,"style":661},[656,660],[567,2365,2367],{"className":2366},[665],[567,2368,2370,2390],{"className":2369},[669,1147],[567,2371,2373,2387],{"className":2372},[673],[567,2374,2376],{"className":2375,"style":1154},[677],[567,2377,2378,2381],{"style":1751},[567,2379],{"className":2380,"style":686},[685],[567,2382,2384],{"className":2383},[690,691,692,693],[567,2385,633],{"className":2386},[656,693],[567,2388,1171],{"className":2389},[1170],[567,2391,2393],{"className":2392},[673],[567,2394,2396],{"className":2395,"style":1178},[677],[567,2397],{},[563,2399,2400,2401,2473,2474,2476],{},"Sind beide ",[567,2402,2404,2423],{"className":2403},[570],[567,2405,2407],{"className":2406},[574],[576,2408,2409],{"xmlns":578},[580,2410,2411,2420],{},[583,2412,2413],{},[1107,2414,2415,2417],{},[589,2416,973],{},[589,2418,2419],{},"i",[635,2421,2422],{"encoding":637},"\\lambda_i",[567,2424,2426],{"className":2425,"ariaHidden":643},[642],[567,2427,2429,2432],{"className":2428},[647],[567,2430],{"className":2431,"style":1236},[651],[567,2433,2435,2438],{"className":2434},[656],[567,2436,973],{"className":2437},[656,660],[567,2439,2441],{"className":2440},[665],[567,2442,2444,2465],{"className":2443},[669,1147],[567,2445,2447,2462],{"className":2446},[673],[567,2448,2451],{"className":2449,"style":2450},[677],"height:0.3117em;",[567,2452,2453,2456],{"style":1157},[567,2454],{"className":2455,"style":686},[685],[567,2457,2459],{"className":2458},[690,691,692,693],[567,2460,2419],{"className":2461},[656,660,693],[567,2463,1171],{"className":2464},[1170],[567,2466,2468],{"className":2467},[673],[567,2469,2471],{"className":2470,"style":1178},[677],[567,2472],{}," negativ, klingt jede Lösung ohne Schwingung ab. In der Physik heißt das ",[1090,2475,551],{}," (starke Dämpfung).",[558,2478,2480],{"id":2479},"beispiele","Beispiele",[563,2482,2483,2656,2657,1397,2724,2823,2824,3041,3042,834,3134,3232],{},[567,2484,2486,2528],{"className":2485},[570],[567,2487,2489],{"className":2488},[574],[576,2490,2491],{"xmlns":578},[580,2492,2493,2525],{},[583,2494,2495,2505,2507,2513,2516,2519,2521,2523],{},[586,2496,2497,2499],{},[589,2498,591],{},[583,2500,2501,2503],{},[595,2502,598],{"mathvariant":597},[595,2504,598],{"mathvariant":597},[595,2506,603],{},[586,2508,2509,2511],{},[589,2510,591],{},[595,2512,598],{"mathvariant":597,"lspace":617,"rspace":617},[595,2514,2515],{},"−",[631,2517,2518],{},"6",[589,2520,591],{},[595,2522,629],{},[631,2524,633],{},[635,2526,2527],{"encoding":637},"y'' + y' - 6y = 0",[567,2529,2531,2578,2625,2647],{"className":2530,"ariaHidden":643},[642],[567,2532,2534,2537,2569,2572,2575],{"className":2533},[647],[567,2535],{"className":2536,"style":652},[651],[567,2538,2540,2543],{"className":2539},[656],[567,2541,591],{"className":2542,"style":661},[656,660],[567,2544,2546],{"className":2545},[665],[567,2547,2549],{"className":2548},[669],[567,2550,2552],{"className":2551},[673],[567,2553,2555],{"className":2554,"style":678},[677],[567,2556,2557,2560],{"style":681},[567,2558],{"className":2559,"style":686},[685],[567,2561,2563],{"className":2562},[690,691,692,693],[567,2564,2566],{"className":2565},[656,693],[567,2567,700],{"className":2568},[656,693],[567,2570],{"className":2571,"style":705},[704],[567,2573,603],{"className":2574},[709],[567,2576],{"className":2577,"style":705},[704],[567,2579,2581,2584,2616,2619,2622],{"className":2580},[647],[567,2582],{"className":2583,"style":652},[651],[567,2585,2587,2590],{"className":2586},[656],[567,2588,591],{"className":2589,"style":661},[656,660],[567,2591,2593],{"className":2592},[665],[567,2594,2596],{"className":2595},[669],[567,2597,2599],{"className":2598},[673],[567,2600,2602],{"className":2601,"style":678},[677],[567,2603,2604,2607],{"style":681},[567,2605],{"className":2606,"style":686},[685],[567,2608,2610],{"className":2609},[690,691,692,693],[567,2611,2613],{"className":2612},[656,693],[567,2614,598],{"className":2615},[656,693],[567,2617],{"className":2618,"style":705},[704],[567,2620,2515],{"className":2621},[709],[567,2623],{"className":2624,"style":705},[704],[567,2626,2628,2632,2635,2638,2641,2644],{"className":2627},[647],[567,2629],{"className":2630,"style":2631},[651],"height:0.8389em;vertical-align:-0.1944em;",[567,2633,2518],{"className":2634},[656],[567,2636,591],{"className":2637,"style":661},[656,660],[567,2639],{"className":2640,"style":786},[704],[567,2642,629],{"className":2643},[790],[567,2645],{"className":2646,"style":786},[704],[567,2648,2650,2653],{"className":2649},[647],[567,2651],{"className":2652,"style":800},[651],[567,2654,633],{"className":2655},[656]," mit ",[567,2658,2660,2685],{"className":2659},[570],[567,2661,2663],{"className":2662},[574],[576,2664,2665],{"xmlns":578},[580,2666,2667,2682],{},[583,2668,2669,2671,2673,2675,2677,2679],{},[589,2670,591],{},[595,2672,1674],{"stretchy":1673},[631,2674,633],{},[595,2676,1679],{"stretchy":1673},[595,2678,629],{},[631,2680,2681],{},"5",[635,2683,2684],{"encoding":637},"y(0) = 5",[567,2686,2688,2715],{"className":2687,"ariaHidden":643},[642],[567,2689,2691,2694,2697,2700,2703,2706,2709,2712],{"className":2690},[647],[567,2692],{"className":2693,"style":1700},[651],[567,2695,591],{"className":2696,"style":661},[656,660],[567,2698,1674],{"className":2699},[1707],[567,2701,633],{"className":2702},[656],[567,2704,1679],{"className":2705},[1714],[567,2707],{"className":2708,"style":786},[704],[567,2710,629],{"className":2711},[790],[567,2713],{"className":2714,"style":786},[704],[567,2716,2718,2721],{"className":2717},[647],[567,2719],{"className":2720,"style":800},[651],[567,2722,2681],{"className":2723},[656],[567,2725,2727,2755],{"className":2726},[570],[567,2728,2730],{"className":2729},[574],[576,2731,2732],{"xmlns":578},[580,2733,2734,2752],{},[583,2735,2736,2742,2744,2746,2748,2750],{},[586,2737,2738,2740],{},[589,2739,591],{},[595,2741,598],{"mathvariant":597,"lspace":617,"rspace":617},[595,2743,1674],{"stretchy":1673},[631,2745,633],{},[595,2747,1679],{"stretchy":1673},[595,2749,629],{},[631,2751,633],{},[635,2753,2754],{"encoding":637},"y'(0) = 0",[567,2756,2758,2814],{"className":2757,"ariaHidden":643},[642],[567,2759,2761,2764,2796,2799,2802,2805,2808,2811],{"className":2760},[647],[567,2762],{"className":2763,"style":1817},[651],[567,2765,2767,2770],{"className":2766},[656],[567,2768,591],{"className":2769,"style":661},[656,660],[567,2771,2773],{"className":2772},[665],[567,2774,2776],{"className":2775},[669],[567,2777,2779],{"className":2778},[673],[567,2780,2782],{"className":2781,"style":678},[677],[567,2783,2784,2787],{"style":681},[567,2785],{"className":2786,"style":686},[685],[567,2788,2790],{"className":2789},[690,691,692,693],[567,2791,2793],{"className":2792},[656,693],[567,2794,598],{"className":2795},[656,693],[567,2797,1674],{"className":2798},[1707],[567,2800,633],{"className":2801},[656],[567,2803,1679],{"className":2804},[1714],[567,2806],{"className":2807,"style":786},[704],[567,2809,629],{"className":2810},[790],[567,2812],{"className":2813,"style":786},[704],[567,2815,2817,2820],{"className":2816},[647],[567,2818],{"className":2819,"style":800},[651],[567,2821,633],{"className":2822},[656],". Die charakteristische Gleichung ",[567,2825,2827,2880],{"className":2826},[570],[567,2828,2830],{"className":2829},[574],[576,2831,2832],{"xmlns":578},[580,2833,2834,2877],{},[583,2835,2836,2842,2844,2846,2848,2850,2852,2854,2856,2858,2860,2862,2864,2866,2868,2871,2873,2875],{},[586,2837,2838,2840],{},[589,2839,973],{},[631,2841,883],{},[595,2843,603],{},[589,2845,973],{},[595,2847,2515],{},[631,2849,2518],{},[595,2851,629],{},[595,2853,1674],{"stretchy":1673},[589,2855,973],{},[595,2857,2515],{},[631,2859,883],{},[595,2861,1679],{"stretchy":1673},[595,2863,1674],{"stretchy":1673},[589,2865,973],{},[595,2867,603],{},[631,2869,2870],{},"3",[595,2872,1679],{"stretchy":1673},[595,2874,629],{},[631,2876,633],{},[635,2878,2879],{"encoding":637},"\\lambda^2 + \\lambda - 6 = (\\lambda - 2)(\\lambda + 3) = 0",[567,2881,2883,2927,2945,2963,2984,3011,3032],{"className":2882,"ariaHidden":643},[642],[567,2884,2886,2889,2918,2921,2924],{"className":2885},[647],[567,2887],{"className":2888,"style":1002},[651],[567,2890,2892,2895],{"className":2891},[656],[567,2893,973],{"className":2894},[656,660],[567,2896,2898],{"className":2897},[665],[567,2899,2901],{"className":2900},[669],[567,2902,2904],{"className":2903},[673],[567,2905,2907],{"className":2906,"style":923},[677],[567,2908,2909,2912],{"style":681},[567,2910],{"className":2911,"style":686},[685],[567,2913,2915],{"className":2914},[690,691,692,693],[567,2916,883],{"className":2917},[656,693],[567,2919],{"className":2920,"style":705},[704],[567,2922,603],{"className":2923},[709],[567,2925],{"className":2926,"style":705},[704],[567,2928,2930,2933,2936,2939,2942],{"className":2929},[647],[567,2931],{"className":2932,"style":1047},[651],[567,2934,973],{"className":2935},[656,660],[567,2937],{"className":2938,"style":705},[704],[567,2940,2515],{"className":2941},[709],[567,2943],{"className":2944,"style":705},[704],[567,2946,2948,2951,2954,2957,2960],{"className":2947},[647],[567,2949],{"className":2950,"style":800},[651],[567,2952,2518],{"className":2953},[656],[567,2955],{"className":2956,"style":786},[704],[567,2958,629],{"className":2959},[790],[567,2961],{"className":2962,"style":786},[704],[567,2964,2966,2969,2972,2975,2978,2981],{"className":2965},[647],[567,2967],{"className":2968,"style":1700},[651],[567,2970,1674],{"className":2971},[1707],[567,2973,973],{"className":2974},[656,660],[567,2976],{"className":2977,"style":705},[704],[567,2979,2515],{"className":2980},[709],[567,2982],{"className":2983,"style":705},[704],[567,2985,2987,2990,2993,2996,2999,3002,3005,3008],{"className":2986},[647],[567,2988],{"className":2989,"style":1700},[651],[567,2991,883],{"className":2992},[656],[567,2994,1679],{"className":2995},[1714],[567,2997,1674],{"className":2998},[1707],[567,3000,973],{"className":3001},[656,660],[567,3003],{"className":3004,"style":705},[704],[567,3006,603],{"className":3007},[709],[567,3009],{"className":3010,"style":705},[704],[567,3012,3014,3017,3020,3023,3026,3029],{"className":3013},[647],[567,3015],{"className":3016,"style":1700},[651],[567,3018,2870],{"className":3019},[656],[567,3021,1679],{"className":3022},[1714],[567,3024],{"className":3025,"style":786},[704],[567,3027,629],{"className":3028},[790],[567,3030],{"className":3031,"style":786},[704],[567,3033,3035,3038],{"className":3034},[647],[567,3036],{"className":3037,"style":800},[651],[567,3039,633],{"className":3040},[656]," liefert ",[567,3043,3045,3067],{"className":3044},[570],[567,3046,3048],{"className":3047},[574],[576,3049,3050],{"xmlns":578},[580,3051,3052,3064],{},[583,3053,3054,3060,3062],{},[1107,3055,3056,3058],{},[589,3057,973],{},[631,3059,1113],{},[595,3061,629],{},[631,3063,883],{},[635,3065,3066],{"encoding":637},"\\lambda_1 = 2",[567,3068,3070,3125],{"className":3069,"ariaHidden":643},[642],[567,3071,3073,3076,3116,3119,3122],{"className":3072},[647],[567,3074],{"className":3075,"style":1236},[651],[567,3077,3079,3082],{"className":3078},[656],[567,3080,973],{"className":3081},[656,660],[567,3083,3085],{"className":3084},[665],[567,3086,3088,3108],{"className":3087},[669,1147],[567,3089,3091,3105],{"className":3090},[673],[567,3092,3094],{"className":3093,"style":1154},[677],[567,3095,3096,3099],{"style":1157},[567,3097],{"className":3098,"style":686},[685],[567,3100,3102],{"className":3101},[690,691,692,693],[567,3103,1113],{"className":3104},[656,693],[567,3106,1171],{"className":3107},[1170],[567,3109,3111],{"className":3110},[673],[567,3112,3114],{"className":3113,"style":1178},[677],[567,3115],{},[567,3117],{"className":3118,"style":786},[704],[567,3120,629],{"className":3121},[790],[567,3123],{"className":3124,"style":786},[704],[567,3126,3128,3131],{"className":3127},[647],[567,3129],{"className":3130,"style":800},[651],[567,3132,883],{"className":3133},[656],[567,3135,3137,3161],{"className":3136},[570],[567,3138,3140],{"className":3139},[574],[576,3141,3142],{"xmlns":578},[580,3143,3144,3158],{},[583,3145,3146,3152,3154,3156],{},[1107,3147,3148,3150],{},[589,3149,973],{},[631,3151,883],{},[595,3153,629],{},[595,3155,2515],{},[631,3157,2870],{},[635,3159,3160],{"encoding":637},"\\lambda_2 = 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= C_1\\,e^{2x} + C_2\\,e^{-3x}",[567,3296,3298,3316,3412],{"className":3297,"ariaHidden":643},[642],[567,3299,3301,3304,3307,3310,3313],{"className":3300},[647],[567,3302],{"className":3303,"style":1730},[651],[567,3305,591],{"className":3306,"style":661},[656,660],[567,3308],{"className":3309,"style":786},[704],[567,3311,629],{"className":3312},[790],[567,3314],{"className":3315,"style":786},[704],[567,3317,3319,3323,3363,3366,3403,3406,3409],{"className":3318},[647],[567,3320],{"className":3321,"style":3322},[651],"height:1.0141em;vertical-align:-0.15em;",[567,3324,3326,3329],{"className":3325},[656],[567,3327,1528],{"className":3328,"style":1550},[656,660],[567,3330,3332],{"className":3331},[665],[567,3333,3335,3355],{"className":3334},[669,1147],[567,3336,3338,3352],{"className":3337},[673],[567,3339,3341],{"className":3340,"style":1154},[677],[567,3342,3343,3346],{"style":1565},[567,3344],{"className":3345,"style":686},[685],[567,3347,3349],{"className":3348},[690,691,692,693],[567,3350,1113],{"className":3351},[656,693],[567,3353,1171],{"className":3354},[1170],[567,3356,3358],{"className":3357},[673],[567,3359,3361],{"className":3360,"style":1178},[677],[567,3362],{},[567,3364],{"className":3365,"style":725},[704],[567,3367,3369,3372],{"className":3368},[656],[567,3370,1294],{"className":3371},[656,660],[567,3373,3375],{"className":3374},[665],[567,3376,3378],{"className":3377},[669],[567,3379,3381],{"className":3380},[673],[567,3382,3385],{"className":3383,"style":3384},[677],"height:0.8641em;",[567,3386,3388,3391],{"style":3387},"top:-3.113em;margin-right:0.05em;",[567,3389],{"className":3390,"style":686},[685],[567,3392,3394],{"className":3393},[690,691,692,693],[567,3395,3397,3400],{"className":3396},[656,693],[567,3398,883],{"className":3399},[656,693],[567,3401,1305],{"className":3402},[656,660,693],[567,3404],{"className":3405,"style":705},[704],[567,3407,603],{"className":3408},[709],[567,3410],{"className":3411,"style":705},[704],[567,3413,3415,3418,3458,3461],{"className":3414},[647],[567,3416],{"className":3417,"style":3322},[651],[567,3419,3421,3424],{"className":3420},[656],[567,3422,1528],{"className":3423,"style":1550},[656,660],[567,3425,3427],{"className":3426},[665],[567,3428,3430,3450],{"className":3429},[669,1147],[567,3431,3433,3447],{"className":3432},[673],[567,3434,3436],{"className":3435,"style":1154},[677],[567,3437,3438,3441],{"style":1565},[567,3439],{"className":3440,"style":686},[685],[567,3442,3444],{"className":3443},[690,691,692,693],[567,3445,883],{"className":3446},[656,693],[567,3448,1171],{"className":3449},[1170],[567,3451,3453],{"className":3452},[673],[567,3454,3456],{"className":3455,"style":1178},[677],[567,3457],{},[567,3459],{"className":3460,"style":725},[704],[567,3462,3464,3467],{"className":3463},[656],[567,3465,1294],{"className":3466},[656,660],[567,3468,3470],{"className":3469},[665],[567,3471,3473],{"className":3472},[669],[567,3474,3476],{"className":3475},[673],[567,3477,3479],{"className":3478,"style":3384},[677],[567,3480,3481,3484],{"style":3387},[567,3482],{"className":3483,"style":686},[685],[567,3485,3487],{"className":3486},[690,691,692,693],[567,3488,3490,3493,3496],{"className":3489},[656,693],[567,3491,2515],{"className":3492},[656,693],[567,3494,2870],{"className":3495},[656,693],[567,3497,1305],{"className":3498},[656,660,693],[563,3500,3501,3502,1397,3657,3822,3823,834,3915,3232],{},"Die Anfangswerte ergeben ",[567,3503,3505,3535],{"className":3504},[570],[567,3506,3508],{"className":3507},[574],[576,3509,3510],{"xmlns":578},[580,3511,3512,3532],{},[583,3513,3514,3520,3522,3528,3530],{},[1107,3515,3516,3518],{},[589,3517,1528],{},[631,3519,1113],{},[595,3521,603],{},[1107,3523,3524,3526],{},[589,3525,1528],{},[631,3527,883],{},[595,3529,629],{},[631,3531,2681],{},[635,3533,3534],{"encoding":637},"C_1 + C_2 = 5",[567,3536,3538,3593,3648],{"className":3537,"ariaHidden":643},[642],[567,3539,3541,3544,3584,3587,3590],{"className":3540},[647],[567,3542],{"className":3543,"style":1543},[651],[567,3545,3547,3550],{"className":3546},[656],[567,3548,1528],{"className":3549,"style":1550},[656,660],[567,3551,3553],{"className":3552},[665],[567,3554,3556,3576],{"className":3555},[669,1147],[567,3557,3559,3573],{"className":3558},[673],[567,3560,3562],{"className":3561,"style":1154},[677],[567,3563,3564,3567],{"style":1565},[567,3565],{"className":3566,"style":686},[685],[567,3568,3570],{"className":3569},[690,691,692,693],[567,3571,1113],{"className":3572},[656,693],[567,3574,1171],{"className":3575},[1170],[567,3577,3579],{"className":3578},[673],[567,3580,3582],{"className":3581,"style":1178},[677],[567,3583],{},[567,3585],{"className":3586,"style":705},[704],[567,3588,603],{"className":3589},[709],[567,3591],{"className":3592,"style":705},[704],[567,3594,3596,3599,3639,3642,3645],{"className":3595},[647],[567,3597],{"className":3598,"style":1543},[651],[567,3600,3602,3605],{"className":3601},[656],[567,3603,1528],{"className":3604,"style":1550},[656,660],[567,3606,3608],{"className":3607},[665],[567,3609,3611,3631],{"className":3610},[669,1147],[567,3612,3614,3628],{"className":3613},[673],[567,3615,3617],{"className":3616,"style":1154},[677],[567,3618,3619,3622],{"style":1565},[567,3620],{"className":3621,"style":686},[685],[567,3623,3625],{"className":3624},[690,691,692,693],[567,3626,883],{"className":3627},[656,693],[567,3629,1171],{"className":3630},[1170],[567,3632,3634],{"className":3633},[673],[567,3635,3637],{"className":3636,"style":1178},[677],[567,3638],{},[567,3640],{"className":3641,"style":786},[704],[567,3643,629],{"className":3644},[790],[567,3646],{"className":3647,"style":786},[704],[567,3649,3651,3654],{"className":3650},[647],[567,3652],{"className":3653,"style":800},[651],[567,3655,2681],{"className":3656},[656],[567,3658,3660,3694],{"className":3659},[570],[567,3661,3663],{"className":3662},[574],[576,3664,3665],{"xmlns":578},[580,3666,3667,3691],{},[583,3668,3669,3671,3677,3679,3681,3687,3689],{},[631,3670,883],{},[1107,3672,3673,3675],{},[589,3674,1528],{},[631,3676,1113],{},[595,3678,2515],{},[631,3680,2870],{},[1107,3682,3683,3685],{},[589,3684,1528],{},[631,3686,883],{},[595,3688,629],{},[631,3690,633],{},[635,3692,3693],{"encoding":637},"2C_1 - 3C_2 = 0",[567,3695,3697,3755,3813],{"className":3696,"ariaHidden":643},[642],[567,3698,3700,3703,3706,3746,3749,3752],{"className":3699},[647],[567,3701],{"className":3702,"style":1543},[651],[567,3704,883],{"className":3705},[656],[567,3707,3709,3712],{"className":3708},[656],[567,3710,1528],{"className":3711,"style":1550},[656,660],[567,3713,3715],{"className":3714},[665],[567,3716,3718,3738],{"className":3717},[669,1147],[567,3719,3721,3735],{"className":3720},[673],[567,3722,3724],{"className":3723,"style":1154},[677],[567,3725,3726,3729],{"style":1565},[567,3727],{"className":3728,"style":686},[685],[567,3730,3732],{"className":3731},[690,691,692,693],[567,3733,1113],{"className":3734},[656,693],[567,3736,1171],{"className":3737},[1170],[567,3739,3741],{"className":3740},[673],[567,3742,3744],{"className":3743,"style":1178},[677],[567,3745],{},[567,3747],{"className":3748,"style":705},[704],[567,3750,2515],{"className":3751},[709],[567,3753],{"className":3754,"style":705},[704],[567,3756,3758,3761,3764,3804,3807,3810],{"className":3757},[647],[567,3759],{"className":3760,"style":1543},[651],[567,3762,2870],{"className":3763},[656],[567,3765,3767,3770],{"className":3766},[656],[567,3768,1528],{"className":3769,"style":1550},[656,660],[567,3771,3773],{"className":3772},[665],[567,3774,3776,3796],{"className":3775},[669,1147],[567,3777,3779,3793],{"className":3778},[673],[567,3780,3782],{"className":3781,"style":1154},[677],[567,3783,3784,3787],{"style":1565},[567,3785],{"className":3786,"style":686},[685],[567,3788,3790],{"className":3789},[690,691,692,693],[567,3791,883],{"className":3792},[656,693],[567,3794,1171],{"className":3795},[1170],[567,3797,3799],{"className":3798},[673],[567,3800,3802],{"className":3801,"style":1178},[677],[567,3803],{},[567,3805],{"className":3806,"style":786},[704],[567,3808,629],{"className":3809},[790],[567,3811],{"className":3812,"style":786},[704],[567,3814,3816,3819],{"className":3815},[647],[567,3817],{"className":3818,"style":800},[651],[567,3820,633],{"className":3821},[656],", also ",[567,3824,3826,3848],{"className":3825},[570],[567,3827,3829],{"className":3828},[574],[576,3830,3831],{"xmlns":578},[580,3832,3833,3845],{},[583,3834,3835,3841,3843],{},[1107,3836,3837,3839],{},[589,3838,1528],{},[631,3840,1113],{},[595,3842,629],{},[631,3844,2870],{},[635,3846,3847],{"encoding":637},"C_1 = 3",[567,3849,3851,3906],{"className":3850,"ariaHidden":643},[642],[567,3852,3854,3857,3897,3900,3903],{"className":3853},[647],[567,3855],{"className":3856,"style":1543},[651],[567,3858,3860,3863],{"className":3859},[656],[567,3861,1528],{"className":3862,"style":1550},[656,660],[567,3864,3866],{"className":3865},[665],[567,3867,3869,3889],{"className":3868},[669,1147],[567,3870,3872,3886],{"className":3871},[673],[567,3873,3875],{"className":3874,"style":1154},[677],[567,3876,3877,3880],{"style":1565},[567,3878],{"className":3879,"style":686},[685],[567,3881,3883],{"className":3882},[690,691,692,693],[567,3884,1113],{"className":3885},[656,693],[567,3887,1171],{"className":3888},[1170],[567,3890,3892],{"className":3891},[673],[567,3893,3895],{"className":3894,"style":1178},[677],[567,3896],{},[567,3898],{"className":3899,"style":786},[704],[567,3901,629],{"className":3902},[790],[567,3904],{"className":3905,"style":786},[704],[567,3907,3909,3912],{"className":3908},[647],[567,3910],{"className":3911,"style":800},[651],[567,3913,2870],{"className":3914},[656],[567,3916,3918,3940],{"className":3917},[570],[567,3919,3921],{"className":3920},[574],[576,3922,3923],{"xmlns":578},[580,3924,3925,3937],{},[583,3926,3927,3933,3935],{},[1107,3928,3929,3931],{},[589,3930,1528],{},[631,3932,883],{},[595,3934,629],{},[631,3936,883],{},[635,3938,3939],{"encoding":637},"C_2 = 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= 3\\,e^{2x} + 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= -1",[567,5075,5077,5132],{"className":5076,"ariaHidden":643},[642],[567,5078,5080,5083,5123,5126,5129],{"className":5079},[647],[567,5081],{"className":5082,"style":1543},[651],[567,5084,5086,5089],{"className":5085},[656],[567,5087,1528],{"className":5088,"style":1550},[656,660],[567,5090,5092],{"className":5091},[665],[567,5093,5095,5115],{"className":5094},[669,1147],[567,5096,5098,5112],{"className":5097},[673],[567,5099,5101],{"className":5100,"style":1154},[677],[567,5102,5103,5106],{"style":1565},[567,5104],{"className":5105,"style":686},[685],[567,5107,5109],{"className":5108},[690,691,692,693],[567,5110,883],{"className":5111},[656,693],[567,5113,1171],{"className":5114},[1170],[567,5116,5118],{"className":5117},[673],[567,5119,5121],{"className":5120,"style":1178},[677],[567,5122],{},[567,5124],{"className":5125,"style":786},[704],[567,5127,629],{"className":5128},[790],[567,5130],{"className":5131,"style":786},[704],[567,5133,5135,5138,5141],{"className":5134},[647],[567,5136],{"className":5137,"style":3225},[651],[567,5139,2515],{"className":5140},[656],[567,5142,1113],{"className":5143},[656],[567,5145,5147],{"className":5146},[1919],[567,5148,5150,5208],{"className":5149},[570],[567,5151,5153],{"className":5152},[574],[576,5154,5155],{"xmlns":578,"display":1928},[580,5156,5157,5205],{},[583,5158,5159,5161,5163,5173,5175,5187,5189,5191,5194,5197,5199,5201,5203],{},[589,5160,591],{},[595,5162,629],{},[586,5164,5165,5167],{},[589,5166,1294],{},[583,5168,5169,5171],{},[631,5170,883],{},[589,5172,1305],{},[595,5174,2515],{},[586,5176,5177,5179],{},[589,5178,1294],{},[583,5180,5181,5183,5185],{},[595,5182,2515],{},[631,5184,883],{},[589,5186,1305],{},[595,5188,629],{},[631,5190,883],{},[589,5192,5193],{},"sinh",[595,5195,5196],{},"⁡",[595,5198,1674],{"stretchy":1673},[631,5200,883],{},[589,5202,1305],{},[595,5204,1679],{"stretchy":1673},[635,5206,5207],{"encoding":637},"y = e^{2x} - e^{-2x} = 2\\sinh(2x)",[567,5209,5211,5229,5279,5332],{"className":5210,"ariaHidden":643},[642],[567,5212,5214,5217,5220,5223,5226],{"className":5213},[647],[567,5215],{"className":5216,"style":1730},[651],[567,5218,591],{"className":5219,"style":661},[656,660],[567,5221],{"className":5222,"style":786},[704],[567,5224,629],{"className":5225},[790],[567,5227],{"className":5228,"style":786},[704],[567,5230,5232,5235,5270,5273,5276],{"className":5231},[647],[567,5233],{"className":5234,"style":4088},[651],[567,5236,5238,5241],{"className":5237},[656],[567,5239,1294],{"className":5240},[656,660],[567,5242,5244],{"className":5243},[665],[567,5245,5247],{"className":5246},[669],[567,5248,5250],{"className":5249},[673],[567,5251,5253],{"className":5252,"style":3384},[677],[567,5254,5255,5258],{"style":3387},[567,5256],{"className":5257,"style":686},[685],[567,5259,5261],{"className":5260},[690,691,692,693],[567,5262,5264,5267],{"className":5263},[656,693],[567,5265,883],{"className":5266},[656,693],[567,5268,1305],{"className":5269},[656,660,693],[567,5271],{"className":5272,"style":705},[704],[567,5274,2515],{"className":5275},[709],[567,5277],{"className":5278,"style":705},[704],[567,5280,5282,5285,5323,5326,5329],{"className":5281},[647],[567,5283],{"className":5284,"style":3384},[651],[567,5286,5288,5291],{"className":5287},[656],[567,5289,1294],{"className":5290},[656,660],[567,5292,5294],{"className":5293},[665],[567,5295,5297],{"className":5296},[669],[567,5298,5300],{"className":5299},[673],[567,5301,5303],{"className":5302,"style":3384},[677],[567,5304,5305,5308],{"style":3387},[567,5306],{"className":5307,"style":686},[685],[567,5309,5311],{"className":5310},[690,691,692,693],[567,5312,5314,5317,5320],{"className":5313},[656,693],[567,5315,2515],{"className":5316},[656,693],[567,5318,883],{"className":5319},[656,693],[567,5321,1305],{"className":5322},[656,660,693],[567,5324],{"className":5325,"style":786},[704],[567,5327,629],{"className":5328},[790],[567,5330],{"className":5331,"style":786},[704],[567,5333,5335,5338,5341,5344,5348,5351,5354,5357],{"className":5334},[647],[567,5336],{"className":5337,"style":1700},[651],[567,5339,883],{"className":5340},[656],[567,5342],{"className":5343,"style":725},[704],[567,5345,5193],{"className":5346},[5347],"mop",[567,5349,1674],{"className":5350},[1707],[567,5352,883],{"className":5353},[656],[567,5355,1305],{"className":5356},[656,660],[567,5358,1679],{"className":5359},[1714],[563,5361,5362,5363,5421,5422,5636],{},"Bei ",[567,5364,5366,5387],{"className":5365},[570],[567,5367,5369],{"className":5368},[574],[576,5370,5371],{"xmlns":578},[580,5372,5373,5384],{},[583,5374,5375,5377,5379,5381],{},[589,5376,973],{},[595,5378,629],{},[595,5380,4594],{},[589,5382,5383],{},"μ",[635,5385,5386],{"encoding":637},"\\lambda = \\pm\\mu",[567,5388,5390,5408],{"className":5389,"ariaHidden":643},[642],[567,5391,5393,5396,5399,5402,5405],{"className":5392},[647],[567,5394],{"className":5395,"style":860},[651],[567,5397,973],{"className":5398},[656,660],[567,5400],{"className":5401,"style":786},[704],[567,5403,629],{"className":5404},[790],[567,5406],{"className":5407,"style":786},[704],[567,5409,5411,5415,5418],{"className":5410},[647],[567,5412],{"className":5413,"style":5414},[651],"height:0.7778em;vertical-align:-0.1944em;",[567,5416,4594],{"className":5417},[656],[567,5419,5383],{"className":5420},[656,660]," schreibt man die Lösung oft gleichwertig als ",[567,5423,5425,5481],{"className":5424},[570],[567,5426,5428],{"className":5427},[574],[576,5429,5430],{"xmlns":578},[580,5431,5432,5478],{},[583,5433,5434,5436,5438,5445,5448,5450,5452,5454,5456,5458,5460,5466,5468,5470,5472,5474,5476],{},[589,5435,591],{},[595,5437,629],{},[1107,5439,5440,5443],{},[589,5441,5442],{},"D",[631,5444,1113],{},[589,5446,5447],{},"cosh",[595,5449,5196],{},[595,5451,1674],{"stretchy":1673},[589,5453,5383],{},[589,5455,1305],{},[595,5457,1679],{"stretchy":1673},[595,5459,603],{},[1107,5461,5462,5464],{},[589,5463,5442],{},[631,5465,883],{},[589,5467,5193],{},[595,5469,5196],{},[595,5471,1674],{"stretchy":1673},[589,5473,5383],{},[589,5475,1305],{},[595,5477,1679],{"stretchy":1673},[635,5479,5480],{"encoding":637},"y = D_1 \\cosh(\\mu x) + D_2 \\sinh(\\mu x)",[567,5482,5484,5502,5575],{"className":5483,"ariaHidden":643},[642],[567,5485,5487,5490,5493,5496,5499],{"className":5486},[647],[567,5488],{"className":5489,"style":1730},[651],[567,5491,591],{"className":5492,"style":661},[656,660],[567,5494],{"className":5495,"style":786},[704],[567,5497,629],{"className":5498},[790],[567,5500],{"className":5501,"style":786},[704],[567,5503,5505,5508,5550,5553,5556,5559,5563,5566,5569,5572],{"className":5504},[647],[567,5506],{"className":5507,"style":1700},[651],[567,5509,5511,5515],{"className":5510},[656],[567,5512,5442],{"className":5513,"style":5514},[656,660],"margin-right:0.0278em;",[567,5516,5518],{"className":5517},[665],[567,5519,5521,5542],{"className":5520},[669,1147],[567,5522,5524,5539],{"className":5523},[673],[567,5525,5527],{"className":5526,"style":1154},[677],[567,5528,5530,5533],{"style":5529},"top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;",[567,5531],{"className":5532,"style":686},[685],[567,5534,5536],{"className":5535},[690,691,692,693],[567,5537,1113],{"className":5538},[656,693],[567,5540,1171],{"className":5541},[1170],[567,5543,5545],{"className":5544},[673],[567,5546,5548],{"className":5547,"style":1178},[677],[567,5549],{},[567,5551],{"className":5552,"style":725},[704],[567,5554,5447],{"className":5555},[5347],[567,5557,1674],{"className":5558},[1707],[567,5560,5562],{"className":5561},[656,660],"μx",[567,5564,1679],{"className":5565},[1714],[567,5567],{"className":5568,"style":705},[704],[567,5570,603],{"className":5571},[709],[567,5573],{"className":5574,"style":705},[704],[567,5576,5578,5581,5621,5624,5627,5630,5633],{"className":5577},[647],[567,5579],{"className":5580,"style":1700},[651],[567,5582,5584,5587],{"className":5583},[656],[567,5585,5442],{"className":5586,"style":5514},[656,660],[567,5588,5590],{"className":5589},[665],[567,5591,5593,5613],{"className":5592},[669,1147],[567,5594,5596,5610],{"className":5595},[673],[567,5597,5599],{"className":5598,"style":1154},[677],[567,5600,5601,5604],{"style":5529},[567,5602],{"className":5603,"style":686},[685],[567,5605,5607],{"className":5606},[690,691,692,693],[567,5608,883],{"className":5609},[656,693],[567,5611,1171],{"className":5612},[1170],[567,5614,5616],{"className":5615},[673],[567,5617,5619],{"className":5618,"style":1178},[677],[567,5620],{},[567,5622],{"className":5623,"style":725},[704],[567,5625,5193],{"className":5626},[5347],[567,5628,1674],{"className":5629},[1707],[567,5631,5562],{"className":5632},[656,660],[567,5634,1679],{"className":5635},[1714],".",[558,5638,5640],{"id":5639},"typische-fehler","Typische Fehler",[5642,5643,5644,6077,6307],"ul",{},[5645,5646,5647,5648,5943,5944,5636],"li",{},"Bei den Anfangswerten die Ableitung falsch bilden: ",[567,5649,5651,5703],{"className":5650},[570],[567,5652,5654],{"className":5653},[574],[576,5655,5656],{"xmlns":578},[580,5657,5658,5700],{},[583,5659,5660,5666,5668,5670,5672,5674,5680,5686,5688,5694],{},[586,5661,5662,5664],{},[589,5663,591],{},[595,5665,598],{"mathvariant":597,"lspace":617,"rspace":617},[595,5667,1674],{"stretchy":1673},[631,5669,633],{},[595,5671,1679],{"stretchy":1673},[595,5673,629],{},[1107,5675,5676,5678],{},[589,5677,973],{},[631,5679,1113],{},[1107,5681,5682,5684],{},[589,5683,1528],{},[631,5685,1113],{},[595,5687,603],{},[1107,5689,5690,5692],{},[589,5691,973],{},[631,5693,883],{},[1107,5695,5696,5698],{},[589,5697,1528],{},[631,5699,883],{},[635,5701,5702],{"encoding":637},"y'(0) = \\lambda_1 C_1 + \\lambda_2 C_2",[567,5704,5706,5762,5857],{"className":5705,"ariaHidden":643},[642],[567,5707,5709,5712,5744,5747,5750,5753,5756,5759],{"className":5708},[647],[567,5710],{"className":5711,"style":1817},[651],[567,5713,5715,5718],{"className":5714},[656],[567,5716,591],{"className":5717,"style":661},[656,660],[567,5719,5721],{"className":5720},[665],[567,5722,5724],{"className":5723},[669],[567,5725,5727],{"className":5726},[673],[567,5728,5730],{"className":5729,"style":678},[677],[567,5731,5732,5735],{"style":681},[567,5733],{"className":5734,"style":686},[685],[567,5736,5738],{"className":5737},[690,691,692,693],[567,5739,5741],{"className":5740},[656,693],[567,5742,598],{"className":5743},[656,693],[567,5745,1674],{"className":5746},[1707],[567,5748,633],{"className":5749},[656],[567,5751,1679],{"className":5752},[1714],[567,5754],{"className":5755,"style":786},[704],[567,5757,629],{"className":5758},[790],[567,5760],{"className":5761,"style":786},[704],[567,5763,5765,5768,5808,5848,5851,5854],{"className":5764},[647],[567,5766],{"className":5767,"style":1236},[651],[567,5769,5771,5774],{"className":5770},[656],[567,5772,973],{"className":5773},[656,660],[567,5775,5777],{"className":5776},[665],[567,5778,5780,5800],{"className":5779},[669,1147],[567,5781,5783,5797],{"className":5782},[673],[567,5784,5786],{"className":5785,"style":1154},[677],[567,5787,5788,5791],{"style":1157},[567,5789],{"className":5790,"style":686},[685],[567,5792,5794],{"className":5793},[690,691,692,693],[567,5795,1113],{"className":5796},[656,693],[567,5798,1171],{"className":5799},[1170],[567,5801,5803],{"className":5802},[673],[567,5804,5806],{"className":5805,"style":1178},[677],[567,5807],{},[567,5809,5811,5814],{"className":5810},[656],[567,5812,1528],{"className":5813,"style":1550},[656,660],[567,5815,5817],{"className":5816},[665],[567,5818,5820,5840],{"className":5819},[669,1147],[567,5821,5823,5837],{"className":5822},[673],[567,5824,5826],{"className":5825,"style":1154},[677],[567,5827,5828,5831],{"style":1565},[567,5829],{"className":5830,"style":686},[685],[567,5832,5834],{"className":5833},[690,691,692,693],[567,5835,1113],{"className":5836},[656,693],[567,5838,1171],{"className":5839},[1170],[567,5841,5843],{"className":5842},[673],[567,5844,5846],{"className":5845,"style":1178},[677],[567,5847],{},[567,5849],{"className":5850,"style":705},[704],[567,5852,603],{"className":5853},[709],[567,5855],{"className":5856,"style":705},[704],[567,5858,5860,5863,5903],{"className":5859},[647],[567,5861],{"className":5862,"style":1236},[651],[567,5864,5866,5869],{"className":5865},[656],[567,5867,973],{"className":5868},[656,660],[567,5870,5872],{"className":5871},[665],[567,5873,5875,5895],{"className":5874},[669,1147],[567,5876,5878,5892],{"className":5877},[673],[567,5879,5881],{"className":5880,"style":1154},[677],[567,5882,5883,5886],{"style":1157},[567,5884],{"className":5885,"style":686},[685],[567,5887,5889],{"className":5888},[690,691,692,693],[567,5890,883],{"className":5891},[656,693],[567,5893,1171],{"className":5894},[1170],[567,5896,5898],{"className":5897},[673],[567,5899,5901],{"className":5900,"style":1178},[677],[567,5902],{},[567,5904,5906,5909],{"className":5905},[656],[567,5907,1528],{"className":5908,"style":1550},[656,660],[567,5910,5912],{"className":5911},[665],[567,5913,5915,5935],{"className":5914},[669,1147],[567,5916,5918,5932],{"className":5917},[673],[567,5919,5921],{"className":5920,"style":1154},[677],[567,5922,5923,5926],{"style":1565},[567,5924],{"className":5925,"style":686},[685],[567,5927,5929],{"className":5928},[690,691,692,693],[567,5930,883],{"className":5931},[656,693],[567,5933,1171],{"className":5934},[1170],[567,5936,5938],{"className":5937},[673],[567,5939,5941],{"className":5940,"style":1178},[677],[567,5942],{},", nicht ",[567,5945,5947,5973],{"className":5946},[570],[567,5948,5950],{"className":5949},[574],[576,5951,5952],{"xmlns":578},[580,5953,5954,5970],{},[583,5955,5956,5962,5964],{},[1107,5957,5958,5960],{},[589,5959,1528],{},[631,5961,1113],{},[595,5963,603],{},[1107,5965,5966,5968],{},[589,5967,1528],{},[631,5969,883],{},[635,5971,5972],{"encoding":637},"C_1 + 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beim Ablesen vertauschen: Aus ",[567,6081,6083,6119],{"className":6082},[570],[567,6084,6086],{"className":6085},[574],[576,6087,6088],{"xmlns":578},[580,6089,6090,6116],{},[583,6091,6092,6094,6096,6098,6100,6102,6104,6106,6108,6110,6112,6114],{},[595,6093,1674],{"stretchy":1673},[589,6095,973],{},[595,6097,2515],{},[631,6099,883],{},[595,6101,1679],{"stretchy":1673},[595,6103,1674],{"stretchy":1673},[589,6105,973],{},[595,6107,603],{},[631,6109,2870],{},[595,6111,1679],{"stretchy":1673},[595,6113,629],{},[631,6115,633],{},[635,6117,6118],{"encoding":637},"(\\lambda - 2)(\\lambda + 3) = 0",[567,6120,6122,6143,6170,6191],{"className":6121,"ariaHidden":643},[642],[567,6123,6125,6128,6131,6134,6137,6140],{"className":6124},[647],[567,6126],{"className":6127,"style":1700},[651],[567,6129,1674],{"className":6130},[1707],[567,6132,973],{"className":6133},[656,660],[567,6135],{"className":6136,"style":705},[704],[567,6138,2515],{"className":6139},[709],[567,6141],{"className":6142,"style":705},[704],[567,6144,6146,6149,6152,6155,6158,6161,6164,6167],{"className":6145},[647],[567,6147],{"className":6148,"style":1700},[651],[567,6150,883],{"className":6151},[656],[567,6153,1679],{"className":6154},[1714],[567,6156,1674],{"className":6157},[1707],[567,6159,973],{"className":6160},[656,660],[567,6162],{"className":6163,"style":705},[704],[567,6165,603],{"className":6166},[709],[567,6168],{"className":6169,"style":705},[704],[567,6171,6173,6176,6179,6182,6185,6188],{"className":6172},[647],[567,6174],{"className":6175,"style":1700},[651],[567,6177,2870],{"className":6178},[656],[567,6180,1679],{"className":6181},[1714],[567,6183],{"className":6184,"style":786},[704],[567,6186,629],{"className":6187},[790],[567,6189],{"className":6190,"style":786},[704],[567,6192,6194,6197],{"className":6193},[647],[567,6195],{"className":6196,"style":800},[651],[567,6198,633],{"className":6199},[656],[567,6201,6203,6221],{"className":6202},[570],[567,6204,6206],{"className":6205},[574],[576,6207,6208],{"xmlns":578},[580,6209,6210,6218],{},[583,6211,6212,6214,6216],{},[589,6213,973],{},[595,6215,629],{},[631,6217,883],{},[635,6219,6220],{"encoding":637},"\\lambda = 2",[567,6222,6224,6242],{"className":6223,"ariaHidden":643},[642],[567,6225,6227,6230,6233,6236,6239],{"className":6226},[647],[567,6228],{"className":6229,"style":860},[651],[567,6231,973],{"className":6232},[656,660],[567,6234],{"className":6235,"style":786},[704],[567,6237,629],{"className":6238},[790],[567,6240],{"className":6241,"style":786},[704],[567,6243,6245,6248],{"className":6244},[647],[567,6246],{"className":6247,"style":800},[651],[567,6249,883],{"className":6250},[656],[567,6252,6254,6274],{"className":6253},[570],[567,6255,6257],{"className":6256},[574],[576,6258,6259],{"xmlns":578},[580,6260,6261,6271],{},[583,6262,6263,6265,6267,6269],{},[589,6264,973],{},[595,6266,629],{},[595,6268,2515],{},[631,6270,2870],{},[635,6272,6273],{"encoding":637},"\\lambda = -3",[567,6275,6277,6295],{"className":6276,"ariaHidden":643},[642],[567,6278,6280,6283,6286,6289,6292],{"className":6279},[647],[567,6281],{"className":6282,"style":860},[651],[567,6284,973],{"className":6285},[656,660],[567,6287],{"className":6288,"style":786},[704],[567,6290,629],{"className":6291},[790],[567,6293],{"className":6294,"style":786},[704],[567,6296,6298,6301,6304],{"className":6297},[647],[567,6299],{"className":6300,"style":3225},[651],[567,6302,2515],{"className":6303},[656],[567,6305,2870],{"className":6306},[656],[5645,6308,6309,6310,6396,6397,1397,6530,6764],{},"Die Formel bei ",[567,6311,6313,6337],{"className":6312},[570],[567,6314,6316],{"className":6315},[574],[576,6317,6318],{"xmlns":578},[580,6319,6320,6334],{},[583,6321,6322,6328,6330,6332],{},[586,6323,6324,6326],{},[589,6325,606],{},[631,6327,883],{},[595,6329,629],{},[631,6331,889],{},[589,6333,622],{},[635,6335,6336],{"encoding":637},"a^2 = 4b",[567,6338,6340,6384],{"className":6339,"ariaHidden":643},[642],[567,6341,6343,6346,6375,6378,6381],{"className":6342},[647],[567,6344],{"className":6345,"style":923},[651],[567,6347,6349,6352],{"className":6348},[656],[567,6350,606],{"className":6351},[656,660],[567,6353,6355],{"className":6354},[665],[567,6356,6358],{"className":6357},[669],[567,6359,6361],{"className":6360},[673],[567,6362,6364],{"className":6363,"style":923},[677],[567,6365,6366,6369],{"style":681},[567,6367],{"className":6368,"style":686},[685],[567,6370,6372],{"className":6371},[690,691,692,693],[567,6373,883],{"className":6374},[656,693],[567,6376],{"className":6377,"style":786},[704],[567,6379,629],{"className":6380},[790],[567,6382],{"className":6383,"style":786},[704],[567,6385,6387,6390,6393],{"className":6386},[647],[567,6388],{"className":6389,"style":860},[651],[567,6391,889],{"className":6392},[656],[567,6394,622],{"className":6395},[656,660]," verwenden: Dann ist ",[567,6398,6400,6426],{"className":6399},[570],[567,6401,6403],{"className":6402},[574],[576,6404,6405],{"xmlns":578},[580,6406,6407,6423],{},[583,6408,6409,6415,6417],{},[1107,6410,6411,6413],{},[589,6412,973],{},[631,6414,1113],{},[595,6416,629],{},[1107,6418,6419,6421],{},[589,6420,973],{},[631,6422,883],{},[635,6424,6425],{"encoding":637},"\\lambda_1 = \\lambda_2",[567,6427,6429,6484],{"className":6428,"ariaHidden":643},[642],[567,6430,6432,6435,6475,6478,6481],{"className":6431},[647],[567,6433],{"className":6434,"style":1236},[651],[567,6436,6438,6441],{"className":6437},[656],[567,6439,973],{"className":6440},[656,660],[567,6442,6444],{"className":6443},[665],[567,6445,6447,6467],{"className":6446},[669,1147],[567,6448,6450,6464],{"className":6449},[673],[567,6451,6453],{"className":6452,"style":1154},[677],[567,6454,6455,6458],{"style":1157},[567,6456],{"className":6457,"style":686},[685],[567,6459,6461],{"className":6460},[690,691,692,693],[567,6462,1113],{"className":6463},[656,693],[567,6465,1171],{"className":6466},[1170],[567,6468,6470],{"className":6469},[673],[567,6471,6473],{"className":6472,"style":1178},[677],[567,6474],{},[567,6476],{"className":6477,"style":786},[704],[567,6479,629],{"className":6480},[790],[567,6482],{"className":6483,"style":786},[704],[567,6485,6487,6490],{"className":6486},[647],[567,6488],{"className":6489,"style":1236},[651],[567,6491,6493,6496],{"className":6492},[656],[567,6494,973],{"className":6495},[656,660],[567,6497,6499],{"className":6498},[665],[567,6500,6502,6522],{"className":6501},[669,1147],[567,6503,6505,6519],{"className":6504},[673],[567,6506,6508],{"className":6507,"style":1154},[677],[567,6509,6510,6513],{"style":1157},[567,6511],{"className":6512,"style":686},[685],[567,6514,6516],{"className":6515},[690,691,692,693],[567,6517,883],{"className":6518},[656,693],[567,6520,1171],{"className":6521},[1170],[567,6523,6525],{"className":6524},[673],[567,6526,6528],{"className":6527,"style":1178},[677],[567,6529],{},[567,6531,6533,6583],{"className":6532},[570],[567,6534,6536],{"className":6535},[574],[576,6537,6538],{"xmlns":578},[580,6539,6540,6580],{},[583,6541,6542,6548,6550,6560,6562,6568,6570],{},[1107,6543,6544,6546],{},[589,6545,1528],{},[631,6547,1113],{},[608,6549,610],{},[586,6551,6552,6554],{},[589,6553,1294],{},[583,6555,6556,6558],{},[589,6557,973],{},[589,6559,1305],{},[595,6561,603],{},[1107,6563,6564,6566],{},[589,6565,1528],{},[631,6567,883],{},[608,6569,610],{},[586,6571,6572,6574],{},[589,6573,1294],{},[583,6575,6576,6578],{},[589,6577,973],{},[589,6579,1305],{},[635,6581,6582],{"encoding":637},"C_1\\,e^{\\lambda x} + C_2\\,e^{\\lambda x}",[567,6584,6586,6680],{"className":6585,"ariaHidden":643},[642],[567,6587,6589,6593,6633,6636,6671,6674,6677],{"className":6588},[647],[567,6590],{"className":6591,"style":6592},[651],"height:0.9991em;vertical-align:-0.15em;",[567,6594,6596,6599],{"className":6595},[656],[567,6597,1528],{"className":6598,"style":1550},[656,660],[567,6600,6602],{"className":6601},[665],[567,6603,6605,6625],{"className":6604},[669,1147],[567,6606,6608,6622],{"className":6607},[673],[567,6609,6611],{"className":6610,"style":1154},[677],[567,6612,6613,6616],{"style":1565},[567,6614],{"className":6615,"style":686},[685],[567,6617,6619],{"className":6618},[690,691,692,693],[567,6620,1113],{"className":6621},[656,693],[567,6623,1171],{"className":6624},[1170],[567,6626,6628],{"className":6627},[673],[567,6629,6631],{"className":6630,"style":1178},[677],[567,6632],{},[567,6634],{"className":6635,"style":725},[704],[567,6637,6639,6642],{"className":6638},[656],[567,6640,1294],{"className":6641},[656,660],[567,6643,6645],{"className":6644},[665],[567,6646,6648],{"className":6647},[669],[567,6649,6651],{"className":6650},[673],[567,6652,6654],{"className":6653,"style":1318},[677],[567,6655,6656,6659],{"style":681},[567,6657],{"className":6658,"style":686},[685],[567,6660,6662],{"className":6661},[690,691,692,693],[567,6663,6665,6668],{"className":6664},[656,693],[567,6666,973],{"className":6667},[656,660,693],[567,6669,1305],{"className":6670},[656,660,693],[567,6672],{"className":6673,"style":705},[704],[567,6675,603],{"className":6676},[709],[567,6678],{"className":6679,"style":705},[704],[567,6681,6683,6686,6726,6729],{"className":6682},[647],[567,6684],{"className":6685,"style":6592},[651],[567,6687,6689,6692],{"className":6688},[656],[567,6690,1528],{"className":6691,"style":1550},[656,660],[567,6693,6695],{"className":6694},[665],[567,6696,6698,6718],{"className":6697},[669,1147],[567,6699,6701,6715],{"className":6700},[673],[567,6702,6704],{"className":6703,"style":1154},[677],[567,6705,6706,6709],{"style":1565},[567,6707],{"className":6708,"style":686},[685],[567,6710,6712],{"className":6711},[690,691,692,693],[567,6713,883],{"className":6714},[656,693],[567,6716,1171],{"className":6717},[1170],[567,6719,6721],{"className":6720},[673],[567,6722,6724],{"className":6723,"style":1178},[677],[567,6725],{},[567,6727],{"className":6728,"style":725},[704],[567,6730,6732,6735],{"className":6731},[656],[567,6733,1294],{"className":6734},[656,660],[567,6736,6738],{"className":6737},[665],[567,6739,6741],{"className":6740},[669],[567,6742,6744],{"className":6743},[673],[567,6745,6747],{"className":6746,"style":1318},[677],[567,6748,6749,6752],{"style":681},[567,6750],{"className":6751,"style":686},[685],[567,6753,6755],{"className":6754},[690,691,692,693],[567,6756,6758,6761],{"className":6757},[656,693],[567,6759,973],{"className":6760},[656,660,693],[567,6762,1305],{"className":6763},[656,660,693]," enthält nur eine freie Konstante.",{"title":6766,"searchDepth":6767,"depth":6767,"links":6768},"",2,[6769,6770,6771],{"id":560,"depth":6767,"text":561},{"id":2479,"depth":6767,"text":2480},{"id":5639,"depth":6767,"text":5640},[6773,6775,6778,6780,6783,6785,6787,6789,6791,6794],{"lhs":6774,"rhs":633},"4*C1*exp(2*x) + 9*C2*exp(-3*x) + (2*C1*exp(2*x) - 3*C2*exp(-3*x)) - 6*(C1*exp(2*x) + C2*exp(-3*x))",{"lhs":6776,"rhs":6777},"l^2 + l - 6","(l - 2)*(l + 3)",{"lhs":6779,"rhs":883},"-1\u002F2 + sqrt(1\u002F4 + 6)",{"lhs":6781,"rhs":6782},"-1\u002F2 - sqrt(1\u002F4 + 6)","-3",{"lhs":6784,"rhs":2681},"3 + 2",{"lhs":6786,"rhs":633},"2*3 - 3*2",{"lhs":6788,"rhs":633},"1 + (-1)",{"lhs":6790,"rhs":889},"2*1 - 2*(-1)",{"lhs":6792,"rhs":6793},"exp(2*x) - exp(-2*x)","2*sinh(2*x)",{"lhs":6795,"rhs":633,"where":6796},"round((exp(2*(x + 0.001)) - exp(-2*(x + 0.001)) - 2*(exp(2*x) - exp(-2*x)) + exp(2*(x - 0.001)) - exp(-2*(x - 0.001)))\u002F0.001^2 - 4*(exp(2*x) - exp(-2*x)), 4)",{"x":6797},0.5,"y'' + a\\,y' + b\\,y = 0,\\ a^2 > 4b,\\ \\lambda_{1,2} = -\\tfrac{a}{2} \\pm \\sqrt{\\tfrac{a^2}{4} - b}","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsup>\u003Cmi>y\u003C\u002Fmi>\u003Cmrow>\u003Cmo mathvariant=\"normal\">′\u003C\u002Fmo>\u003Cmo mathvariant=\"normal\">′\u003C\u002Fmo>\u003C\u002Fmrow>\u003C\u002Fmsup>\u003Cmo>+\u003C\u002Fmo>\u003Cmi>a\u003C\u002Fmi>\u003Cmtext> \u003C\u002Fmtext>\u003Cmsup>\u003Cmi>y\u003C\u002Fmi>\u003Cmo mathvariant=\"normal\" lspace=\"0em\" rspace=\"0em\">′\u003C\u002Fmo>\u003C\u002Fmsup>\u003Cmo>+\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003Cmtext> \u003C\u002Fmtext>\u003Cmi>y\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">y'' + a\\,y' + b\\,y = 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