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x)\\bigr)",[568,1680,1682,1744,1820],{"className":1681,"ariaHidden":644},[643],[568,1683,1685,1688,1735,1738,1741],{"className":1684},[648],[568,1686],{"className":1687,"style":1546},[652],[568,1689,1691,1694],{"className":1690},[657],[568,1692,1513],{"className":1693},[657,661],[568,1695,1697],{"className":1696},[666],[568,1698,1700],{"className":1699},[670],[568,1701,1703],{"className":1702},[674],[568,1704,1706],{"className":1705,"style":1546},[678],[568,1707,1708,1711],{"style":682},[568,1709],{"className":1710,"style":687},[686],[568,1712,1714],{"className":1713},[691,692,693,694],[568,1715,1717,1720,1723,1726,1729,1732],{"className":1716},[657,694],[568,1718,1519],{"className":1719},[1215,694],[568,1721,999],{"className":1722,"style":1151},[657,661,694],[568,1724,604],{"className":1725},[710,694],[568,1727,1588],{"className":1728,"style":662},[657,661,694],[568,1730,1530],{"className":1731},[1281,694],[568,1733,1533],{"className":1734},[657,661,694],[568,1736],{"className":1737,"style":787},[705],[568,1739,630],{"className":1740},[791],[568,1742],{"className":1743,"style":787},[705],[568,1745,1747,1751,1787,1795,1799,1802,1805,1808,1811,1814,1817],{"className":1746},[648],[568,1748],{"className":1749,"style":1750},[652],"height:1.2em;vertical-align:-0.35em;",[568,1752,1754,1757],{"className":1753},[657],[568,1755,1513],{"className":1756},[657,661],[568,1758,1760],{"className":1759},[666],[568,1761,1763],{"className":1762},[670],[568,1764,1766],{"className":1765},[674],[568,1767,1770],{"className":1768,"style":1769},[678],"height:0.6644em;",[568,1771,1772,1775],{"style":682},[568,1773],{"className":1774,"style":687},[686],[568,1776,1778],{"className":1777},[691,692,693,694],[568,1779,1781,1784],{"className":1780},[657,694],[568,1782,999],{"className":1783,"style":1151},[657,661,694],[568,1785,1533],{"className":1786},[657,661,694],[568,1788,1790],{"className":1789},[1215],[568,1791,1519],{"className":1792},[1793,1794],"delimsizing","size1",[568,1796,1645],{"className":1797},[1798],"mop",[568,1800,1519],{"className":1801},[1215],[568,1803,1010],{"className":1804,"style":662},[657,661],[568,1806,1533],{"className":1807},[657,661],[568,1809,1530],{"className":1810},[1281],[568,1812],{"className":1813,"style":706},[705],[568,1815,604],{"className":1816},[710],[568,1818],{"className":1819,"style":706},[705],[568,1821,1823,1826,1829,1832,1835,1838,1841,1844,1847],{"className":1822},[648],[568,1824],{"className":1825,"style":1750},[652],[568,1827,1005],{"className":1828},[657,661],[568,1830],{"className":1831,"style":726},[705],[568,1833,1663],{"className":1834},[1798],[568,1836,1519],{"className":1837},[1215],[568,1839,1010],{"className":1840,"style":662},[657,661],[568,1842,1533],{"className":1843},[657,661],[568,1845,1530],{"className":1846},[1281],[568,1848,1850],{"className":1849},[1281],[568,1851,1530],{"className":1852},[1793,1794],". Real- und Imaginärteil sind jeweils reelle Lösungen, nämlich ",[568,1855,1857,1891],{"className":1856},[571],[568,1858,1860],{"className":1859},[575],[577,1861,1862],{"xmlns":579},[581,1863,1864,1888],{},[584,1865,1866,1876,1878,1880,1882,1884,1886],{},[587,1867,1868,1870],{},[590,1869,1513],{},[584,1871,1872,1874],{},[590,1873,999],{},[590,1875,1533],{},[590,1877,1645],{},[596,1879,1648],{},[596,1881,1519],{"stretchy":1518},[590,1883,1010],{},[590,1885,1533],{},[596,1887,1530],{"stretchy":1518},[636,1889,1890],{"encoding":638},"e^{\\alpha x}\\cos(\\omega x)",[568,1892,1894],{"className":1893,"ariaHidden":644},[643],[568,1895,1897,1901,1936,1939,1942,1945,1948,1951],{"className":1896},[648],[568,1898],{"className":1899,"style":1900},[652],"height:1em;vertical-align:-0.25em;",[568,1902,1904,1907],{"className":1903},[657],[568,1905,1513],{"className":1906},[657,661],[568,1908,1910],{"className":1909},[666],[568,1911,1913],{"className":1912},[670],[568,1914,1916],{"className":1915},[674],[568,1917,1919],{"className":1918,"style":1769},[678],[568,1920,1921,1924],{"style":682},[568,1922],{"className":1923,"style":687},[686],[568,1925,1927],{"className":1926},[691,692,693,694],[568,1928,1930,1933],{"className":1929},[657,694],[568,1931,999],{"className":1932,"style":1151},[657,661,694],[568,1934,1533],{"className":1935},[657,661,694],[568,1937],{"className":1938,"style":726},[705],[568,1940,1645],{"className":1941},[1798],[568,1943,1519],{"className":1944},[1215],[568,1946,1010],{"className":1947,"style":662},[657,661],[568,1949,1533],{"className":1950},[657,661],[568,1952,1530],{"className":1953},[1281]," und ",[568,1956,1958,1992],{"className":1957},[571],[568,1959,1961],{"className":1960},[575],[577,1962,1963],{"xmlns":579},[581,1964,1965,1989],{},[584,1966,1967,1977,1979,1981,1983,1985,1987],{},[587,1968,1969,1971],{},[590,1970,1513],{},[584,1972,1973,1975],{},[590,1974,999],{},[590,1976,1533],{},[590,1978,1663],{},[596,1980,1648],{},[596,1982,1519],{"stretchy":1518},[590,1984,1010],{},[590,1986,1533],{},[596,1988,1530],{"stretchy":1518},[636,1990,1991],{"encoding":638},"e^{\\alpha x}\\sin(\\omega x)",[568,1993,1995],{"className":1994,"ariaHidden":644},[643],[568,1996,1998,2001,2036,2039,2042,2045,2048,2051],{"className":1997},[648],[568,1999],{"className":2000,"style":1900},[652],[568,2002,2004,2007],{"className":2003},[657],[568,2005,1513],{"className":2006},[657,661],[568,2008,2010],{"className":2009},[666],[568,2011,2013],{"className":2012},[670],[568,2014,2016],{"className":2015},[674],[568,2017,2019],{"className":2018,"style":1769},[678],[568,2020,2021,2024],{"style":682},[568,2022],{"className":2023,"style":687},[686],[568,2025,2027],{"className":2026},[691,692,693,694],[568,2028,2030,2033],{"className":2029},[657,694],[568,2031,999],{"className":2032,"style":1151},[657,661,694],[568,2034,1533],{"className":2035},[657,661,694],[568,2037],{"className":2038,"style":726},[705],[568,2040,1663],{"className":2041},[1798],[568,2043,1519],{"className":2044},[1215],[568,2046,1010],{"className":2047,"style":662},[657,661],[568,2049,1533],{"className":2050},[657,661],[568,2052,1530],{"className":2053},[1281],". Daraus setzt sich die allgemeine reelle Lösung zusammen.",[564,2056,2057,2058,2061,2062,2091,2092,2161],{},"Die Lösung ist eine ",[959,2059,2060],{},"Schwingung"," mit der Kreisfrequenz ",[568,2063,2065,2079],{"className":2064},[571],[568,2066,2068],{"className":2067},[575],[577,2069,2070],{"xmlns":579},[581,2071,2072,2076],{},[584,2073,2074],{},[590,2075,1010],{},[636,2077,2078],{"encoding":638},"\\omega",[568,2080,2082],{"className":2081,"ariaHidden":644},[643],[568,2083,2085,2088],{"className":2084},[648],[568,2086],{"className":2087,"style":831},[652],[568,2089,1010],{"className":2090,"style":662},[657,661],", deren Amplitude sich wie ",[568,2093,2095,2117],{"className":2094},[571],[568,2096,2098],{"className":2097},[575],[577,2099,2100],{"xmlns":579},[581,2101,2102,2114],{},[584,2103,2104],{},[587,2105,2106,2108],{},[590,2107,1513],{},[584,2109,2110,2112],{},[590,2111,999],{},[590,2113,1533],{},[636,2115,2116],{"encoding":638},"e^{\\alpha x}",[568,2118,2120],{"className":2119,"ariaHidden":644},[643],[568,2121,2123,2126],{"className":2122},[648],[568,2124],{"className":2125,"style":1769},[652],[568,2127,2129,2132],{"className":2128},[657],[568,2130,1513],{"className":2131},[657,661],[568,2133,2135],{"className":2134},[666],[568,2136,2138],{"className":2137},[670],[568,2139,2141],{"className":2140},[674],[568,2142,2144],{"className":2143,"style":1769},[678],[568,2145,2146,2149],{"style":682},[568,2147],{"className":2148,"style":687},[686],[568,2150,2152],{"className":2151},[691,692,693,694],[568,2153,2155,2158],{"className":2154},[657,694],[568,2156,999],{"className":2157,"style":1151},[657,661,694],[568,2159,1533],{"className":2160},[657,661,694]," verhält:",[2163,2164,2165,2221,2275],"ul",{},[2166,2167,2168,2220],"li",{},[568,2169,2171,2189],{"className":2170},[571],[568,2172,2174],{"className":2173},[575],[577,2175,2176],{"xmlns":579},[581,2177,2178,2186],{},[584,2179,2180,2182,2184],{},[590,2181,999],{},[596,2183,887],{},[632,2185,634],{},[636,2187,2188],{"encoding":638},"\\alpha \u003C 0",[568,2190,2192,2211],{"className":2191,"ariaHidden":644},[643],[568,2193,2195,2199,2202,2205,2208],{"className":2194},[648],[568,2196],{"className":2197,"style":2198},[652],"height:0.5782em;vertical-align:-0.0391em;",[568,2200,999],{"className":2201,"style":1151},[657,661],[568,2203],{"className":2204,"style":787},[705],[568,2206,887],{"className":2207},[791],[568,2209],{"className":2210,"style":787},[705],[568,2212,2214,2217],{"className":2213},[648],[568,2215],{"className":2216,"style":801},[652],[568,2218,634],{"className":2219},[657],": gedämpfte Schwingung, die abklingt.",[2166,2222,2223,2274],{},[568,2224,2226,2244],{"className":2225},[571],[568,2227,2229],{"className":2228},[575],[577,2230,2231],{"xmlns":579},[581,2232,2233,2241],{},[584,2234,2235,2237,2239],{},[590,2236,999],{},[596,2238,630],{},[632,2240,634],{},[636,2242,2243],{"encoding":638},"\\alpha = 0",[568,2245,2247,2265],{"className":2246,"ariaHidden":644},[643],[568,2248,2250,2253,2256,2259,2262],{"className":2249},[648],[568,2251],{"className":2252,"style":831},[652],[568,2254,999],{"className":2255,"style":1151},[657,661],[568,2257],{"className":2258,"style":787},[705],[568,2260,630],{"className":2261},[791],[568,2263],{"className":2264,"style":787},[705],[568,2266,2268,2271],{"className":2267},[648],[568,2269],{"className":2270,"style":801},[652],[568,2272,634],{"className":2273},[657],": ungedämpfte Schwingung mit konstanter Amplitude.",[2166,2276,2277,2328],{},[568,2278,2280,2298],{"className":2279},[571],[568,2281,2283],{"className":2282},[575],[577,2284,2285],{"xmlns":579},[581,2286,2287,2295],{},[584,2288,2289,2291,2293],{},[590,2290,999],{},[596,2292,1060],{},[632,2294,634],{},[636,2296,2297],{"encoding":638},"\\alpha > 0",[568,2299,2301,2319],{"className":2300,"ariaHidden":644},[643],[568,2302,2304,2307,2310,2313,2316],{"className":2303},[648],[568,2305],{"className":2306,"style":2198},[652],[568,2308,999],{"className":2309,"style":1151},[657,661],[568,2311],{"className":2312,"style":787},[705],[568,2314,1060],{"className":2315},[791],[568,2317],{"className":2318,"style":787},[705],[568,2320,2322,2325],{"className":2321},[648],[568,2323],{"className":2324,"style":801},[652],[568,2326,634],{"className":2327},[657],": aufschaukelnde Schwingung.",[564,2330,2331,2332,1954,2444,2658],{},"Die Anfangswerte ergeben ",[568,2333,2335,2364],{"className":2334},[571],[568,2336,2338],{"className":2337},[575],[577,2339,2340],{"xmlns":579},[581,2341,2342,2361],{},[584,2343,2344,2351,2353,2355,2357,2359],{},[980,2345,2346,2349],{},[590,2347,2348],{},"C",[632,2350,989],{},[596,2352,630],{},[590,2354,592],{},[596,2356,1519],{"stretchy":1518},[632,2358,634],{},[596,2360,1530],{"stretchy":1518},[636,2362,2363],{"encoding":638},"C_1 = y(0)",[568,2365,2367,2426],{"className":2366,"ariaHidden":644},[643],[568,2368,2370,2374,2417,2420,2423],{"className":2369},[648],[568,2371],{"className":2372,"style":2373},[652],"height:0.8333em;vertical-align:-0.15em;",[568,2375,2377,2381],{"className":2376},[657],[568,2378,2348],{"className":2379,"style":2380},[657,661],"margin-right:0.0715em;",[568,2382,2384],{"className":2383},[666],[568,2385,2387,2408],{"className":2386},[670,1088],[568,2388,2390,2405],{"className":2389},[674],[568,2391,2393],{"className":2392,"style":1095},[678],[568,2394,2396,2399],{"style":2395},"top:-2.55em;margin-left:-0.0715em;margin-right:0.05em;",[568,2397],{"className":2398,"style":687},[686],[568,2400,2402],{"className":2401},[691,692,693,694],[568,2403,989],{"className":2404},[657,694],[568,2406,1122],{"className":2407},[1121],[568,2409,2411],{"className":2410},[674],[568,2412,2415],{"className":2413,"style":2414},[678],"height:0.15em;",[568,2416],{},[568,2418],{"className":2419,"style":787},[705],[568,2421,630],{"className":2422},[791],[568,2424],{"className":2425,"style":787},[705],[568,2427,2429,2432,2435,2438,2441],{"className":2428},[648],[568,2430],{"className":2431,"style":1900},[652],[568,2433,592],{"className":2434,"style":662},[657,661],[568,2436,1519],{"className":2437},[1215],[568,2439,634],{"className":2440},[657],[568,2442,1530],{"className":2443},[1281],[568,2445,2447,2491],{"className":2446},[571],[568,2448,2450],{"className":2449},[575],[577,2451,2452],{"xmlns":579},[581,2453,2454,2488],{},[584,2455,2456,2458,2464,2466,2468,2474,2476,2482,2484,2486],{},[590,2457,999],{},[980,2459,2460,2462],{},[590,2461,2348],{},[632,2463,989],{},[596,2465,604],{},[590,2467,1010],{},[980,2469,2470,2472],{},[590,2471,2348],{},[632,2473,884],{},[596,2475,630],{},[587,2477,2478,2480],{},[590,2479,592],{},[596,2481,599],{"mathvariant":598,"lspace":618,"rspace":618},[596,2483,1519],{"stretchy":1518},[632,2485,634],{},[596,2487,1530],{"stretchy":1518},[636,2489,2490],{"encoding":638},"\\alpha C_1 + \\omega C_2 = y'(0)",[568,2492,2494,2552,2610],{"className":2493,"ariaHidden":644},[643],[568,2495,2497,2500,2503,2543,2546,2549],{"className":2496},[648],[568,2498],{"className":2499,"style":2373},[652],[568,2501,999],{"className":2502,"style":1151},[657,661],[568,2504,2506,2509],{"className":2505},[657],[568,2507,2348],{"className":2508,"style":2380},[657,661],[568,2510,2512],{"className":2511},[666],[568,2513,2515,2535],{"className":2514},[670,1088],[568,2516,2518,2532],{"className":2517},[674],[568,2519,2521],{"className":2520,"style":1095},[678],[568,2522,2523,2526],{"style":2395},[568,2524],{"className":2525,"style":687},[686],[568,2527,2529],{"className":2528},[691,692,693,694],[568,2530,989],{"className":2531},[657,694],[568,2533,1122],{"className":2534},[1121],[568,2536,2538],{"className":2537},[674],[568,2539,2541],{"className":2540,"style":2414},[678],[568,2542],{},[568,2544],{"className":2545,"style":706},[705],[568,2547,604],{"className":2548},[710],[568,2550],{"className":2551,"style":706},[705],[568,2553,2555,2558,2561,2601,2604,2607],{"className":2554},[648],[568,2556],{"className":2557,"style":2373},[652],[568,2559,1010],{"className":2560,"style":662},[657,661],[568,2562,2564,2567],{"className":2563},[657],[568,2565,2348],{"className":2566,"style":2380},[657,661],[568,2568,2570],{"className":2569},[666],[568,2571,2573,2593],{"className":2572},[670,1088],[568,2574,2576,2590],{"className":2575},[674],[568,2577,2579],{"className":2578,"style":1095},[678],[568,2580,2581,2584],{"style":2395},[568,2582],{"className":2583,"style":687},[686],[568,2585,2587],{"className":2586},[691,692,693,694],[568,2588,884],{"className":2589},[657,694],[568,2591,1122],{"className":2592},[1121],[568,2594,2596],{"className":2595},[674],[568,2597,2599],{"className":2598,"style":2414},[678],[568,2600],{},[568,2602],{"className":2603,"style":787},[705],[568,2605,630],{"className":2606},[791],[568,2608],{"className":2609,"style":787},[705],[568,2611,2613,2617,2649,2652,2655],{"className":2612},[648],[568,2614],{"className":2615,"style":2616},[652],"height:1.0019em;vertical-align:-0.25em;",[568,2618,2620,2623],{"className":2619},[657],[568,2621,592],{"className":2622,"style":662},[657,661],[568,2624,2626],{"className":2625},[666],[568,2627,2629],{"className":2628},[670],[568,2630,2632],{"className":2631},[674],[568,2633,2635],{"className":2634,"style":679},[678],[568,2636,2637,2640],{"style":682},[568,2638],{"className":2639,"style":687},[686],[568,2641,2643],{"className":2642},[691,692,693,694],[568,2644,2646],{"className":2645},[657,694],[568,2647,599],{"className":2648},[657,694],[568,2650,1519],{"className":2651},[1215],[568,2653,634],{"className":2654},[657],[568,2656,1530],{"className":2657},[1281],".",[559,2660,2662],{"id":2661},"beispiele","Beispiele",[564,2664,2665,2842,2843,835,2909,3008,3009,3141],{},[568,2666,2668,2711],{"className":2667},[571],[568,2669,2671],{"className":2670},[575],[577,2672,2673],{"xmlns":579},[581,2674,2675,2708],{},[584,2676,2677,2687,2689,2691,2697,2699,2702,2704,2706],{},[587,2678,2679,2681],{},[590,2680,592],{},[584,2682,2683,2685],{},[596,2684,599],{"mathvariant":598},[596,2686,599],{"mathvariant":598},[596,2688,604],{},[632,2690,884],{},[587,2692,2693,2695],{},[590,2694,592],{},[596,2696,599],{"mathvariant":598,"lspace":618,"rspace":618},[596,2698,604],{},[632,2700,2701],{},"5",[590,2703,592],{},[596,2705,630],{},[632,2707,634],{},[636,2709,2710],{"encoding":638},"y'' + 2y' + 5y = 0",[568,2712,2714,2761,2811,2833],{"className":2713,"ariaHidden":644},[643],[568,2715,2717,2720,2752,2755,2758],{"className":2716},[648],[568,2718],{"className":2719,"style":653},[652],[568,2721,2723,2726],{"className":2722},[657],[568,2724,592],{"className":2725,"style":662},[657,661],[568,2727,2729],{"className":2728},[666],[568,2730,2732],{"className":2731},[670],[568,2733,2735],{"className":2734},[674],[568,2736,2738],{"className":2737,"style":679},[678],[568,2739,2740,2743],{"style":682},[568,2741],{"className":2742,"style":687},[686],[568,2744,2746],{"className":2745},[691,692,693,694],[568,2747,2749],{"className":2748},[657,694],[568,2750,701],{"className":2751},[657,694],[568,2753],{"className":2754,"style":706},[705],[568,2756,604],{"className":2757},[710],[568,2759],{"className":2760,"style":706},[705],[568,2762,2764,2767,2770,2802,2805,2808],{"className":2763},[648],[568,2765],{"className":2766,"style":653},[652],[568,2768,884],{"className":2769},[657],[568,2771,2773,2776],{"className":2772},[657],[568,2774,592],{"className":2775,"style":662},[657,661],[568,2777,2779],{"className":2778},[666],[568,2780,2782],{"className":2781},[670],[568,2783,2785],{"className":2784},[674],[568,2786,2788],{"className":2787,"style":679},[678],[568,2789,2790,2793],{"style":682},[568,2791],{"className":2792,"style":687},[686],[568,2794,2796],{"className":2795},[691,692,693,694],[568,2797,2799],{"className":2798},[657,694],[568,2800,599],{"className":2801},[657,694],[568,2803],{"className":2804,"style":706},[705],[568,2806,604],{"className":2807},[710],[568,2809],{"className":2810,"style":706},[705],[568,2812,2814,2818,2821,2824,2827,2830],{"className":2813},[648],[568,2815],{"className":2816,"style":2817},[652],"height:0.8389em;vertical-align:-0.1944em;",[568,2819,2701],{"className":2820},[657],[568,2822,592],{"className":2823,"style":662},[657,661],[568,2825],{"className":2826,"style":787},[705],[568,2828,630],{"className":2829},[791],[568,2831],{"className":2832,"style":787},[705],[568,2834,2836,2839],{"className":2835},[648],[568,2837],{"className":2838,"style":801},[652],[568,2840,634],{"className":2841},[657]," 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= e^{-x}\\bigl(C_1 \\cos(2x) + C_2 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= 1",[568,3884,3886,3941],{"className":3885,"ariaHidden":644},[643],[568,3887,3889,3892,3932,3935,3938],{"className":3888},[648],[568,3890],{"className":3891,"style":2373},[652],[568,3893,3895,3898],{"className":3894},[657],[568,3896,2348],{"className":3897,"style":2380},[657,661],[568,3899,3901],{"className":3900},[666],[568,3902,3904,3924],{"className":3903},[670,1088],[568,3905,3907,3921],{"className":3906},[674],[568,3908,3910],{"className":3909,"style":1095},[678],[568,3911,3912,3915],{"style":2395},[568,3913],{"className":3914,"style":687},[686],[568,3916,3918],{"className":3917},[691,692,693,694],[568,3919,989],{"className":3920},[657,694],[568,3922,1122],{"className":3923},[1121],[568,3925,3927],{"className":3926},[674],[568,3928,3930],{"className":3929,"style":2414},[678],[568,3931],{},[568,3933],{"className":3934,"style":787},[705],[568,3936,630],{"className":3937},[791],[568,3939],{"className":3940,"style":787},[705],[568,3942,3944,3947],{"className":3943},[648],[568,3945],{"className":3946,"style":801},[652],[568,3948,989],{"className":3949},[657],[568,3951,3953,3987],{"className":3952},[571],[568,3954,3956],{"className":3955},[575],[577,3957,3958],{"xmlns":579},[581,3959,3960,3984],{},[584,3961,3962,3964,3970,3972,3974,3980,3982],{},[596,3963,1022],{},[980,3965,3966,3968],{},[590,3967,2348],{},[632,3969,989],{},[596,3971,604],{},[632,3973,884],{},[980,3975,3976,3978],{},[590,3977,2348],{},[632,3979,884],{},[596,3981,630],{},[632,3983,989],{},[636,3985,3986],{"encoding":638},"-C_1 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1",[568,3988,3990,4048,4106],{"className":3989,"ariaHidden":644},[643],[568,3991,3993,3996,3999,4039,4042,4045],{"className":3992},[648],[568,3994],{"className":3995,"style":2373},[652],[568,3997,1022],{"className":3998},[657],[568,4000,4002,4005],{"className":4001},[657],[568,4003,2348],{"className":4004,"style":2380},[657,661],[568,4006,4008],{"className":4007},[666],[568,4009,4011,4031],{"className":4010},[670,1088],[568,4012,4014,4028],{"className":4013},[674],[568,4015,4017],{"className":4016,"style":1095},[678],[568,4018,4019,4022],{"style":2395},[568,4020],{"className":4021,"style":687},[686],[568,4023,4025],{"className":4024},[691,692,693,694],[568,4026,989],{"className":4027},[657,694],[568,4029,1122],{"className":4030},[1121],[568,4032,4034],{"className":4033},[674],[568,4035,4037],{"className":4036,"style":2414},[678],[568,4038],{},[568,4040],{"className":4041,"style":706},[705],[568,4043,604],{"className":4044},[710],[568,4046],{"className":4047,"style":706},[705],[568,4049,4051,4054,4057,4097,4100,4103],{"className":4050},[648],[568,4052],{"className":4053,"style":2373},[652],[568,4055,884],{"className":4056},[657],[568,4058,4060,4063],{"className":4059},[657],[568,4061,2348],{"className":4062,"style":2380},[657,661],[568,4064,4066],{"className":4065},[666],[568,4067,4069,4089],{"className":4068},[670,1088],[568,4070,4072,4086],{"className":4071},[674],[568,4073,4075],{"className":4074,"style":1095},[678],[568,4076,4077,4080],{"style":2395},[568,4078],{"className":4079,"style":687},[686],[568,4081,4083],{"className":4082},[691,692,693,694],[568,4084,884],{"className":4085},[657,694],[568,4087,1122],{"className":4088},[1121],[568,4090,4092],{"className":4091},[674],[568,4093,4095],{"className":4094,"style":2414},[678],[568,4096],{},[568,4098],{"className":4099,"style":787},[705],[568,4101,630],{"className":4102},[791],[568,4104],{"className":4105,"style":787},[705],[568,4107,4109,4112],{"className":4108},[648],[568,4110],{"className":4111,"style":801},[652],[568,4113,989],{"className":4114},[657]," folgt ",[568,4117,4119,4141],{"className":4118},[571],[568,4120,4122],{"className":4121},[575],[577,4123,4124],{"xmlns":579},[581,4125,4126,4138],{},[584,4127,4128,4134,4136],{},[980,4129,4130,4132],{},[590,4131,2348],{},[632,4133,884],{},[596,4135,630],{},[632,4137,989],{},[636,4139,4140],{"encoding":638},"C_2 = 1",[568,4142,4144,4199],{"className":4143,"ariaHidden":644},[643],[568,4145,4147,4150,4190,4193,4196],{"className":4146},[648],[568,4148],{"className":4149,"style":2373},[652],[568,4151,4153,4156],{"className":4152},[657],[568,4154,2348],{"className":4155,"style":2380},[657,661],[568,4157,4159],{"className":4158},[666],[568,4160,4162,4182],{"className":4161},[670,1088],[568,4163,4165,4179],{"className":4164},[674],[568,4166,4168],{"className":4167,"style":1095},[678],[568,4169,4170,4173],{"style":2395},[568,4171],{"className":4172,"style":687},[686],[568,4174,4176],{"className":4175},[691,692,693,694],[568,4177,884],{"className":4178},[657,694],[568,4180,1122],{"className":4181},[1121],[568,4183,4185],{"className":4184},[674],[568,4186,4188],{"className":4187,"style":2414},[678],[568,4189],{},[568,4191],{"className":4192,"style":787},[705],[568,4194,630],{"className":4195},[791],[568,4197],{"className":4198,"style":787},[705],[568,4200,4202,4205],{"className":4201},[648],[568,4203],{"className":4204,"style":801},[652],[568,4206,989],{"className":4207},[657],":",[568,4210,4212],{"className":4211},[965],[568,4213,4215,4271],{"className":4214},[571],[568,4216,4218],{"className":4217},[575],[577,4219,4220],{"xmlns":579,"display":974},[581,4221,4222,4268],{},[584,4223,4224,4226,4228,4238,4240,4242,4244,4246,4248,4250,4252,4254,4256,4258,4260,4262,4264,4266],{},[590,4225,592],{},[596,4227,630],{},[587,4229,4230,4232],{},[590,4231,1513],{},[584,4233,4234,4236],{},[596,4235,1022],{},[590,4237,1533],{},[596,4239,1519],{"fence":644,"stretchy":644,"minsize":1642,"maxsize":1642},[590,4241,1645],{},[596,4243,1648],{},[596,4245,1519],{"stretchy":1518},[632,4247,884],{},[590,4249,1533],{},[596,4251,1530],{"stretchy":1518},[596,4253,604],{},[590,4255,1663],{},[596,4257,1648],{},[596,4259,1519],{"stretchy":1518},[632,4261,884],{},[590,4263,1533],{},[596,4265,1530],{"stretchy":1518},[596,4267,1530],{"fence":644,"stretchy":644,"minsize":1642,"maxsize":1642},[636,4269,4270],{"encoding":638},"y = e^{-x} \\bigl( \\cos(2x) + \\sin(2x) \\bigr)",[568,4272,4274,4292,4365],{"className":4273,"ariaHidden":644},[643],[568,4275,4277,4280,4283,4286,4289],{"className":4276},[648],[568,4278],{"className":4279,"style":3660},[652],[568,4281,592],{"className":4282,"style":662},[657,661],[568,4284],{"className":4285,"style":787},[705],[568,4287,630],{"className":4288},[791],[568,4290],{"className":4291,"style":787},[705],[568,4293,4295,4298,4335,4341,4344,4347,4350,4353,4356,4359,4362],{"className":4294},[648],[568,4296],{"className":4297,"style":1750},[652],[568,4299,4301,4304],{"className":4300},[657],[568,4302,1513],{"className":4303},[657,661],[568,4305,4307],{"className":4306},[666],[568,4308,4310],{"className":4309},[670],[568,4311,4313],{"className":4312},[674],[568,4314,4317],{"className":4315,"style":4316},[678],"height:0.8213em;",[568,4318,4320,4323],{"style":4319},"top:-3.113em;margin-right:0.05em;",[568,4321],{"className":4322,"style":687},[686],[568,4324,4326],{"className":4325},[691,692,693,694],[568,4327,4329,4332],{"className":4328},[657,694],[568,4330,1022],{"className":4331},[657,694],[568,4333,1533],{"className":4334},[657,661,694],[568,4336,4338],{"className":4337},[1215],[568,4339,1519],{"className":4340},[1793,1794],[568,4342,1645],{"className":4343},[1798],[568,4345,1519],{"className":4346},[1215],[568,4348,884],{"className":4349},[657],[568,4351,1533],{"className":4352},[657,661],[568,4354,1530],{"className":4355},[1281],[568,4357],{"className":4358,"style":706},[705],[568,4360,604],{"className":4361},[710],[568,4363],{"className":4364,"style":706},[705],[568,4366,4368,4371,4374,4377,4380,4383,4386],{"className":4367},[648],[568,4369],{"className":4370,"style":1750},[652],[568,4372,1663],{"className":4373},[1798],[568,4375,1519],{"className":4376},[1215],[568,4378,884],{"className":4379},[657],[568,4381,1533],{"className":4382},[657,661],[568,4384,1530],{"className":4385},[1281],[568,4387,4389],{"className":4388},[1281],[568,4390,1530],{"className":4391},[1793,1794],[564,4393,4394,4510,4511,4614,4615,2842,4678,4208],{},[568,4395,4397,4430],{"className":4396},[571],[568,4398,4400],{"className":4399},[575],[577,4401,4402],{"xmlns":579},[581,4403,4404,4427],{},[584,4405,4406,4416,4418,4421,4423,4425],{},[587,4407,4408,4410],{},[590,4409,592],{},[584,4411,4412,4414],{},[596,4413,599],{"mathvariant":598},[596,4415,599],{"mathvariant":598},[596,4417,604],{},[632,4419,4420],{},"9",[590,4422,592],{},[596,4424,630],{},[632,4426,634],{},[636,4428,4429],{"encoding":638},"y'' + 9y = 0",[568,4431,4433,4480,4501],{"className":4432,"ariaHidden":644},[643],[568,4434,4436,4439,4471,4474,4477],{"className":4435},[648],[568,4437],{"className":4438,"style":653},[652],[568,4440,4442,4445],{"className":4441},[657],[568,4443,592],{"className":4444,"style":662},[657,661],[568,4446,4448],{"className":4447},[666],[568,4449,4451],{"className":4450},[670],[568,4452,4454],{"className":4453},[674],[568,4455,4457],{"className":4456,"style":679},[678],[568,4458,4459,4462],{"style":682},[568,4460],{"className":4461,"style":687},[686],[568,4463,4465],{"className":4464},[691,692,693,694],[568,4466,4468],{"className":4467},[657,694],[568,4469,701],{"className":4470},[657,694],[568,4472],{"className":4473,"style":706},[705],[568,4475,604],{"className":4476},[710],[568,4478],{"className":4479,"style":706},[705],[568,4481,4483,4486,4489,4492,4495,4498],{"className":4482},[648],[568,4484],{"className":4485,"style":2817},[652],[568,4487,4420],{"className":4488},[657],[568,4490,592],{"className":4491,"style":662},[657,661],[568,4493],{"className":4494,"style":787},[705],[568,4496,630],{"className":4497},[791],[568,4499],{"className":4500,"style":787},[705],[568,4502,4504,4507],{"className":4503},[648],[568,4505],{"className":4506,"style":801},[652],[568,4508,634],{"className":4509},[657]," führt auf ",[568,4512,4514,4540],{"className":4513},[571],[568,4515,4517],{"className":4516},[575],[577,4518,4519],{"xmlns":579},[581,4520,4521,4537],{},[584,4522,4523,4529,4531,4533,4535],{},[587,4524,4525,4527],{},[590,4526,984],{},[632,4528,884],{},[596,4530,604],{},[632,4532,4420],{},[596,4534,630],{},[632,4536,634],{},[636,4538,4539],{"encoding":638},"\\lambda^2 + 9 = 0",[568,4541,4543,4587,4605],{"className":4542,"ariaHidden":644},[643],[568,4544,4546,4549,4578,4581,4584],{"className":4545},[648],[568,4547],{"className":4548,"style":3053},[652],[568,4550,4552,4555],{"className":4551},[657],[568,4553,984],{"className":4554},[657,661],[568,4556,4558],{"className":4557},[666],[568,4559,4561],{"className":4560},[670],[568,4562,4564],{"className":4563},[674],[568,4565,4567],{"className":4566,"style":924},[678],[568,4568,4569,4572],{"style":682},[568,4570],{"className":4571,"style":687},[686],[568,4573,4575],{"className":4574},[691,692,693,694],[568,4576,884],{"className":4577},[657,694],[568,4579],{"className":4580,"style":706},[705],[568,4582,604],{"className":4583},[710],[568,4585],{"className":4586,"style":706},[705],[568,4588,4590,4593,4596,4599,4602],{"className":4589},[648],[568,4591],{"className":4592,"style":801},[652],[568,4594,4420],{"className":4595},[657],[568,4597],{"className":4598,"style":787},[705],[568,4600,630],{"className":4601},[791],[568,4603],{"className":4604,"style":787},[705],[568,4606,4608,4611],{"className":4607},[648],[568,4609],{"className":4610,"style":801},[652],[568,4612,634],{"className":4613},[657],", also ",[568,4616,4618,4641],{"className":4617},[571],[568,4619,4621],{"className":4620},[575],[577,4622,4623],{"xmlns":579},[581,4624,4625,4638],{},[584,4626,4627,4629,4631,4633,4636],{},[590,4628,984],{},[596,4630,630],{},[596,4632,1002],{},[632,4634,4635],{},"3",[590,4637,1005],{},[636,4639,4640],{"encoding":638},"\\lambda = \\pm 3i",[568,4642,4644,4662],{"className":4643,"ariaHidden":644},[643],[568,4645,4647,4650,4653,4656,4659],{"className":4646},[648],[568,4648],{"className":4649,"style":861},[652],[568,4651,984],{"className":4652},[657,661],[568,4654],{"className":4655,"style":787},[705],[568,4657,630],{"className":4658},[791],[568,4660],{"className":4661,"style":787},[705],[568,4663,4665,4669,4672,4675],{"className":4664},[648],[568,4666],{"className":4667,"style":4668},[652],"height:0.7429em;vertical-align:-0.0833em;",[568,4670,1002],{"className":4671},[657],[568,4673,4635],{"className":4674},[657],[568,4676,1005],{"className":4677},[657,661],[568,4679,4681,4698],{"className":4680},[571],[568,4682,4684],{"className":4683},[575],[577,4685,4686],{"xmlns":579},[581,4687,4688,4696],{},[584,4689,4690,4692,4694],{},[590,4691,999],{},[596,4693,630],{},[632,4695,634],{},[636,4697,2243],{"encoding":638},[568,4699,4701,4719],{"className":4700,"ariaHidden":644},[643],[568,4702,4704,4707,4710,4713,4716],{"className":4703},[648],[568,4705],{"className":4706,"style":831},[652],[568,4708,999],{"className":4709,"style":1151},[657,661],[568,4711],{"className":4712,"style":787},[705],[568,4714,630],{"className":4715},[791],[568,4717],{"className":4718,"style":787},[705],[568,4720,4722,4725],{"className":4721},[648],[568,4723],{"className":4724,"style":801},[652],[568,4726,634],{"className":4727},[657],[568,4729,4731],{"className":4730},[965],[568,4732,4734,4788],{"className":4733},[571],[568,4735,4737],{"className":4736},[575],[577,4738,4739],{"xmlns":579,"display":974},[581,4740,4741,4785],{},[584,4742,4743,4745,4747,4753,4755,4757,4759,4761,4763,4765,4767,4773,4775,4777,4779,4781,4783],{},[590,4744,592],{},[596,4746,630],{},[980,4748,4749,4751],{},[590,4750,2348],{},[632,4752,989],{},[590,4754,1645],{},[596,4756,1648],{},[596,4758,1519],{"stretchy":1518},[632,4760,4635],{},[590,4762,1533],{},[596,4764,1530],{"stretchy":1518},[596,4766,604],{},[980,4768,4769,4771],{},[590,4770,2348],{},[632,4772,884],{},[590,4774,1663],{},[596,4776,1648],{},[596,4778,1519],{"stretchy":1518},[632,4780,4635],{},[590,4782,1533],{},[596,4784,1530],{"stretchy":1518},[636,4786,4787],{"encoding":638},"y = C_1 \\cos(3x) + C_2 \\sin(3x)",[568,4789,4791,4809,4882],{"className":4790,"ariaHidden":644},[643],[568,4792,4794,4797,4800,4803,4806],{"className":4793},[648],[568,4795],{"className":4796,"style":3660},[652],[568,4798,592],{"className":4799,"style":662},[657,661],[568,4801],{"className":4802,"style":787},[705],[568,4804,630],{"className":4805},[791],[568,4807],{"className":4808,"style":787},[705],[568,4810,4812,4815,4855,4858,4861,4864,4867,4870,4873,4876,4879],{"className":4811},[648],[568,4813],{"className":4814,"style":1900},[652],[568,4816,4818,4821],{"className":4817},[657],[568,4819,2348],{"className":4820,"style":2380},[657,661],[568,4822,4824],{"className":4823},[666],[568,4825,4827,4847],{"className":4826},[670,1088],[568,4828,4830,4844],{"className":4829},[674],[568,4831,4833],{"className":4832,"style":1095},[678],[568,4834,4835,4838],{"style":2395},[568,4836],{"className":4837,"style":687},[686],[568,4839,4841],{"className":4840},[691,692,693,694],[568,4842,989],{"className":4843},[657,694],[568,4845,1122],{"className":4846},[1121],[568,4848,4850],{"className":4849},[674],[568,4851,4853],{"className":4852,"style":2414},[678],[568,4854],{},[568,4856],{"className":4857,"style":726},[705],[568,4859,1645],{"className":4860},[1798],[568,4862,1519],{"className":4863},[1215],[568,4865,4635],{"className":4866},[657],[568,4868,1533],{"className":4869},[657,661],[568,4871,1530],{"className":4872},[1281],[568,4874],{"className":4875,"style":706},[705],[568,4877,604],{"className":4878},[710],[568,4880],{"className":4881,"style":706},[705],[568,4883,4885,4888,4928,4931,4934,4937,4940,4943],{"className":4884},[648],[568,4886],{"className":4887,"style":1900},[652],[568,4889,4891,4894],{"className":4890},[657],[568,4892,2348],{"className":4893,"style":2380},[657,661],[568,4895,4897],{"className":4896},[666],[568,4898,4900,4920],{"className":4899},[670,1088],[568,4901,4903,4917],{"className":4902},[674],[568,4904,4906],{"className":4905,"style":1095},[678],[568,4907,4908,4911],{"style":2395},[568,4909],{"className":4910,"style":687},[686],[568,4912,4914],{"className":4913},[691,692,693,694],[568,4915,884],{"className":4916},[657,694],[568,4918,1122],{"className":4919},[1121],[568,4921,4923],{"className":4922},[674],[568,4924,4926],{"className":4925,"style":2414},[678],[568,4927],{},[568,4929],{"className":4930,"style":726},[705],[568,4932,1663],{"className":4933},[1798],[568,4935,1519],{"className":4936},[1215],[568,4938,4635],{"className":4939},[657],[568,4941,1533],{"className":4942},[657,661],[568,4944,1530],{"className":4945},[1281],[564,4947,4948,4949,2658],{},"Das ist eine ungedämpfte Schwingung mit der Periode ",[568,4950,4952,4975],{"className":4951},[571],[568,4953,4955],{"className":4954},[575],[577,4956,4957],{"xmlns":579},[581,4958,4959,4972],{},[584,4960,4961],{},[1024,4962,4963,4970],{},[584,4964,4965,4967],{},[632,4966,884],{},[590,4968,4969],{},"π",[632,4971,4635],{},[636,4973,4974],{"encoding":638},"\\frac{2\\pi}{3}",[568,4976,4978],{"className":4977,"ariaHidden":644},[643],[568,4979,4981,4985],{"className":4980},[648],[568,4982],{"className":4983,"style":4984},[652],"height:1.1901em;vertical-align:-0.345em;",[568,4986,4988,4991,5057],{"className":4987},[657],[568,4989],{"className":4990},[1215,1216],[568,4992,4994],{"className":4993},[1024],[568,4995,4997,5048],{"className":4996},[670,1088],[568,4998,5000,5045],{"className":4999},[674],[568,5001,5004,5019,5027],{"className":5002,"style":5003},[678],"height:0.8451em;",[568,5005,5007,5010],{"style":5006},"top:-2.655em;",[568,5008],{"className":5009,"style":1236},[686],[568,5011,5013],{"className":5012},[691,692,693,694],[568,5014,5016],{"className":5015},[657,694],[568,5017,4635],{"className":5018},[657,694],[568,5020,5021,5024],{"style":1245},[568,5022],{"className":5023,"style":1236},[686],[568,5025],{"className":5026,"style":1253},[1252],[568,5028,5030,5033],{"style":5029},"top:-3.394em;",[568,5031],{"className":5032,"style":1236},[686],[568,5034,5036],{"className":5035},[691,692,693,694],[568,5037,5039,5042],{"className":5038},[657,694],[568,5040,884],{"className":5041},[657,694],[568,5043,4969],{"className":5044,"style":662},[657,661,694],[568,5046,1122],{"className":5047},[1121],[568,5049,5051],{"className":5050},[674],[568,5052,5055],{"className":5053,"style":5054},[678],"height:0.345em;",[568,5056],{},[568,5058],{"className":5059},[1281,1216],[559,5061,5063],{"id":5062},"typische-fehler","Typische Fehler",[2163,5065,5066,5519,5624,5696],{},[2166,5067,5068,5096,5097,5326,5327,2658],{},[568,5069,5071,5084],{"className":5070},[571],[568,5072,5074],{"className":5073},[575],[577,5075,5076],{"xmlns":579},[581,5077,5078,5082],{},[584,5079,5080],{},[590,5081,1010],{},[636,5083,2078],{"encoding":638},[568,5085,5087],{"className":5086,"ariaHidden":644},[643],[568,5088,5090,5093],{"className":5089},[648],[568,5091],{"className":5092,"style":831},[652],[568,5094,1010],{"className":5095,"style":662},[657,661]," mit Vorzeichen oder aus der falschen Wurzel bilden: ",[568,5098,5100,5134],{"className":5099},[571],[568,5101,5103],{"className":5102},[575],[577,5104,5105],{"xmlns":579},[581,5106,5107,5131],{},[584,5108,5109,5111,5113],{},[590,5110,1010],{},[596,5112,630],{},[1040,5114,5115],{},[584,5116,5117,5119,5121],{},[590,5118,623],{},[596,5120,1022],{},[1024,5122,5123,5129],{},[587,5124,5125,5127],{},[590,5126,607],{},[632,5128,884],{},[632,5130,890],{},[636,5132,5133],{"encoding":638},"\\omega = \\sqrt{b - \\frac{a^2}{4}}",[568,5135,5137,5155],{"className":5136,"ariaHidden":644},[643],[568,5138,5140,5143,5146,5149,5152],{"className":5139},[648],[568,5141],{"className":5142,"style":831},[652],[568,5144,1010],{"className":5145,"style":662},[657,661],[568,5147],{"className":5148,"style":787},[705],[568,5150,630],{"className":5151},[791],[568,5153],{"className":5154,"style":787},[705],[568,5156,5158,5162],{"className":5157},[648],[568,5159],{"className":5160,"style":5161},[652],"height:1.84em;vertical-align:-0.5693em;",[568,5163,5165],{"className":5164},[657,1314],[568,5166,5168,5317],{"className":5167},[670,1088],[568,5169,5171,5314],{"className":5170},[674],[568,5172,5175,5297],{"className":5173,"style":5174},[678],"height:1.2707em;",[568,5176,5179,5183],{"className":5177,"style":5178},[1328],"top:-3.8em;",[568,5180],{"className":5181,"style":5182},[686],"height:3.8em;",[568,5184,5186,5189,5192,5195,5198],{"className":5185,"style":1337},[657],[568,5187,623],{"className":5188},[657,661],[568,5190],{"className":5191,"style":706},[705],[568,5193,1022],{"className":5194},[710],[568,5196],{"className":5197,"style":706},[705],[568,5199,5201,5204,5294],{"className":5200},[657],[568,5202],{"className":5203},[1215,1216],[568,5205,5207],{"className":5206},[1024],[568,5208,5210,5286],{"className":5209},[670,1088],[568,5211,5213,5283],{"className":5212},[674],[568,5214,5217,5231,5239],{"className":5215,"style":5216},[678],"height:0.9164em;",[568,5218,5219,5222],{"style":5006},[568,5220],{"className":5221,"style":1236},[686],[568,5223,5225],{"className":5224},[691,692,693,694],[568,5226,5228],{"className":5227},[657,694],[568,5229,890],{"className":5230},[657,694],[568,5232,5233,5236],{"style":1245},[568,5234],{"className":5235,"style":1236},[686],[568,5237],{"className":5238,"style":1253},[1252],[568,5240,5241,5244],{"style":5029},[568,5242],{"className":5243,"style":1236},[686],[568,5245,5247],{"className":5246},[691,692,693,694],[568,5248,5250],{"className":5249},[657,694],[568,5251,5253,5256],{"className":5252},[657,694],[568,5254,607],{"className":5255},[657,661,694],[568,5257,5259],{"className":5258},[666],[568,5260,5262],{"className":5261},[670],[568,5263,5265],{"className":5264},[674],[568,5266,5269],{"className":5267,"style":5268},[678],"height:0.7463em;",[568,5270,5272,5276],{"style":5271},"top:-2.786em;margin-right:0.0714em;",[568,5273],{"className":5274,"style":5275},[686],"height:2.5em;",[568,5277,5280],{"className":5278},[691,5279,1794,694],"reset-size3",[568,5281,884],{"className":5282},[657,694],[568,5284,1122],{"className":5285},[1121],[568,5287,5289],{"className":5288},[674],[568,5290,5292],{"className":5291,"style":5054},[678],[568,5293],{},[568,5295],{"className":5296},[1281,1216],[568,5298,5300,5303],{"style":5299},"top:-3.2307em;",[568,5301],{"className":5302,"style":5182},[686],[568,5304,5307],{"className":5305,"style":5306},[1450],"min-width:1.02em;height:1.88em;",[1453,5308,5311],{"xmlns":1455,"width":1456,"height":5309,"viewBox":5310,"preserveAspectRatio":1459},"1.88em","0 0 400000 1944",[1461,5312],{"d":5313},"M983 90\nl0 -0\nc4,-6.7,10,-10,18,-10 H400000v40\nH1013.1s-83.4,268,-264.1,840c-180.7,572,-277,876.3,-289,913c-4.7,4.7,-12.7,7,-24,7\ns-12,0,-12,0c-1.3,-3.3,-3.7,-11.7,-7,-25c-35.3,-125.3,-106.7,-373.3,-214,-744\nc-10,12,-21,25,-33,39s-32,39,-32,39c-6,-5.3,-15,-14,-27,-26s25,-30,25,-30\nc26.7,-32.7,52,-63,76,-91s52,-60,52,-60s208,722,208,722\nc56,-175.3,126.3,-397.3,211,-666c84.7,-268.7,153.8,-488.2,207.5,-658.5\nc53.7,-170.3,84.5,-266.8,92.5,-289.5z\nM1001 80h400000v40h-400000z",[568,5315,1122],{"className":5316},[1121],[568,5318,5320],{"className":5319},[674],[568,5321,5324],{"className":5322,"style":5323},[678],"height:0.5693em;",[568,5325],{},", nicht ",[568,5328,5330,5360],{"className":5329},[571],[568,5331,5333],{"className":5332},[575],[577,5334,5335],{"xmlns":579},[581,5336,5337,5357],{},[584,5338,5339],{},[1040,5340,5341],{},[584,5342,5343,5353,5355],{},[1024,5344,5345,5351],{},[587,5346,5347,5349],{},[590,5348,607],{},[632,5350,884],{},[632,5352,890],{},[596,5354,1022],{},[590,5356,623],{},[636,5358,5359],{"encoding":638},"\\sqrt{\\frac{a^2}{4} - b}",[568,5361,5363],{"className":5362,"ariaHidden":644},[643],[568,5364,5366,5369],{"className":5365},[648],[568,5367],{"className":5368,"style":5161},[652],[568,5370,5372],{"className":5371},[657,1314],[568,5373,5375,5511],{"className":5374},[670,1088],[568,5376,5378,5508],{"className":5377},[674],[568,5379,5381,5496],{"className":5380,"style":5174},[678],[568,5382,5384,5387],{"className":5383,"style":5178},[1328],[568,5385],{"className":5386,"style":5182},[686],[568,5388,5390,5484,5487,5490,5493],{"className":5389,"style":1337},[657],[568,5391,5393,5396,5481],{"className":5392},[657],[568,5394],{"className":5395},[1215,1216],[568,5397,5399],{"className":5398},[1024],[568,5400,5402,5473],{"className":5401},[670,1088],[568,5403,5405,5470],{"className":5404},[674],[568,5406,5408,5422,5430],{"className":5407,"style":5216},[678],[568,5409,5410,5413],{"style":5006},[568,5411],{"className":5412,"style":1236},[686],[568,5414,5416],{"className":5415},[691,692,693,694],[568,5417,5419],{"className":5418},[657,694],[568,5420,890],{"className":5421},[657,694],[568,5423,5424,5427],{"style":1245},[568,5425],{"className":5426,"style":1236},[686],[568,5428],{"className":5429,"style":1253},[1252],[568,5431,5432,5435],{"style":5029},[568,5433],{"className":5434,"style":1236},[686],[568,5436,5438],{"className":5437},[691,692,693,694],[568,5439,5441],{"className":5440},[657,694],[568,5442,5444,5447],{"className":5443},[657,694],[568,5445,607],{"className":5446},[657,661,694],[568,5448,5450],{"className":5449},[666],[568,5451,5453],{"className":5452},[670],[568,5454,5456],{"className":5455},[674],[568,5457,5459],{"className":5458,"style":5268},[678],[568,5460,5461,5464],{"style":5271},[568,5462],{"className":5463,"style":5275},[686],[568,5465,5467],{"className":5466},[691,5279,1794,694],[568,5468,884],{"className":5469},[657,694],[568,5471,1122],{"className":5472},[1121],[568,5474,5476],{"className":5475},[674],[568,5477,5479],{"className":5478,"style":5054},[678],[568,5480],{},[568,5482],{"className":5483},[1281,1216],[568,5485],{"className":5486,"style":706},[705],[568,5488,1022],{"className":5489},[710],[568,5491],{"className":5492,"style":706},[705],[568,5494,623],{"className":5495},[657,661],[568,5497,5498,5501],{"style":5299},[568,5499],{"className":5500,"style":5182},[686],[568,5502,5504],{"className":5503,"style":5306},[1450],[1453,5505,5506],{"xmlns":1455,"width":1456,"height":5309,"viewBox":5310,"preserveAspectRatio":1459},[1461,5507],{"d":5313},[568,5509,1122],{"className":5510},[1121],[568,5512,5514],{"className":5513},[674],[568,5515,5517],{"className":5516,"style":5323},[678],[568,5518],{},[2166,5520,5521,5522,5623],{},"Die komplexe Lösung ",[568,5523,5525,5561],{"className":5524},[571],[568,5526,5528],{"className":5527},[575],[577,5529,5530],{"xmlns":579},[581,5531,5532,5558],{},[584,5533,5534,5536,5538],{},[590,5535,2348],{},[609,5537,611],{},[587,5539,5540,5542],{},[590,5541,1513],{},[584,5543,5544,5546,5548,5550,5552,5554,5556],{},[596,5545,1519],{"stretchy":1518},[590,5547,999],{},[596,5549,604],{},[590,5551,1005],{},[590,5553,1010],{},[596,5555,1530],{"stretchy":1518},[590,5557,1533],{},[636,5559,5560],{"encoding":638},"C\\,e^{(\\alpha + i\\omega)x}",[568,5562,5564],{"className":5563,"ariaHidden":644},[643],[568,5565,5567,5570,5573,5576],{"className":5566},[648],[568,5568],{"className":5569,"style":1546},[652],[568,5571,2348],{"className":5572,"style":2380},[657,661],[568,5574],{"className":5575,"style":726},[705],[568,5577,5579,5582],{"className":5578},[657],[568,5580,1513],{"className":5581},[657,661],[568,5583,5585],{"className":5584},[666],[568,5586,5588],{"className":5587},[670],[568,5589,5591],{"className":5590},[674],[568,5592,5594],{"className":5593,"style":1546},[678],[568,5595,5596,5599],{"style":682},[568,5597],{"className":5598,"style":687},[686],[568,5600,5602],{"className":5601},[691,692,693,694],[568,5603,5605,5608,5611,5614,5617,5620],{"className":5604},[657,694],[568,5606,1519],{"className":5607},[1215,694],[568,5609,999],{"className":5610,"style":1151},[657,661,694],[568,5612,604],{"className":5613},[710,694],[568,5615,1588],{"className":5616,"style":662},[657,661,694],[568,5618,1530],{"className":5619},[1281,694],[568,5621,1533],{"className":5622},[657,661,694]," als Endergebnis stehen lassen, obwohl eine reelle Lösung gesucht ist.",[2166,5625,5626,5627,5695],{},"Den Faktor ",[568,5628,5630,5651],{"className":5629},[571],[568,5631,5633],{"className":5632},[575],[577,5634,5635],{"xmlns":579},[581,5636,5637,5649],{},[584,5638,5639],{},[587,5640,5641,5643],{},[590,5642,1513],{},[584,5644,5645,5647],{},[590,5646,999],{},[590,5648,1533],{},[636,5650,2116],{"encoding":638},[568,5652,5654],{"className":5653,"ariaHidden":644},[643],[568,5655,5657,5660],{"className":5656},[648],[568,5658],{"className":5659,"style":1769},[652],[568,5661,5663,5666],{"className":5662},[657],[568,5664,1513],{"className":5665},[657,661],[568,5667,5669],{"className":5668},[666],[568,5670,5672],{"className":5671},[670],[568,5673,5675],{"className":5674},[674],[568,5676,5678],{"className":5677,"style":1769},[678],[568,5679,5680,5683],{"style":682},[568,5681],{"className":5682,"style":687},[686],[568,5684,5686],{"className":5685},[691,692,693,694],[568,5687,5689,5692],{"className":5688},[657,694],[568,5690,999],{"className":5691,"style":1151},[657,661,694],[568,5693,1533],{"className":5694},[657,661,694]," nur vor den Kosinus schreiben: Er gehört vor die ganze Klammer.",[2166,5697,5698,5699,5776,5777,5845,5846,6059,6060,2658],{},"Bei ",[568,5700,5702,5726],{"className":5701},[571],[568,5703,5705],{"className":5704},[575],[577,5706,5707],{"xmlns":579},[581,5708,5709,5723],{},[584,5710,5711,5717,5719,5721],{},[587,5712,5713,5715],{},[590,5714,592],{},[596,5716,599],{"mathvariant":598,"lspace":618,"rspace":618},[596,5718,1519],{"stretchy":1518},[632,5720,634],{},[596,5722,1530],{"stretchy":1518},[636,5724,5725],{"encoding":638},"y'(0)",[568,5727,5729],{"className":5728,"ariaHidden":644},[643],[568,5730,5732,5735,5767,5770,5773],{"className":5731},[648],[568,5733],{"className":5734,"style":2616},[652],[568,5736,5738,5741],{"className":5737},[657],[568,5739,592],{"className":5740,"style":662},[657,661],[568,5742,5744],{"className":5743},[666],[568,5745,5747],{"className":5746},[670],[568,5748,5750],{"className":5749},[674],[568,5751,5753],{"className":5752,"style":679},[678],[568,5754,5755,5758],{"style":682},[568,5756],{"className":5757,"style":687},[686],[568,5759,5761],{"className":5760},[691,692,693,694],[568,5762,5764],{"className":5763},[657,694],[568,5765,599],{"className":5766},[657,694],[568,5768,1519],{"className":5769},[1215],[568,5771,634],{"className":5772},[657],[568,5774,1530],{"className":5775},[1281]," den Anteil von ",[568,5778,5780,5801],{"className":5779},[571],[568,5781,5783],{"className":5782},[575],[577,5784,5785],{"xmlns":579},[581,5786,5787,5799],{},[584,5788,5789],{},[587,5790,5791,5793],{},[590,5792,1513],{},[584,5794,5795,5797],{},[590,5796,999],{},[590,5798,1533],{},[636,5800,2116],{"encoding":638},[568,5802,5804],{"className":5803,"ariaHidden":644},[643],[568,5805,5807,5810],{"className":5806},[648],[568,5808],{"className":5809,"style":1769},[652],[568,5811,5813,5816],{"className":5812},[657],[568,5814,1513],{"className":5815},[657,661],[568,5817,5819],{"className":5818},[666],[568,5820,5822],{"className":5821},[670],[568,5823,5825],{"className":5824},[674],[568,5826,5828],{"className":5827,"style":1769},[678],[568,5829,5830,5833],{"style":682},[568,5831],{"className":5832,"style":687},[686],[568,5834,5836],{"className":5835},[691,692,693,694],[568,5837,5839,5842],{"className":5838},[657,694],[568,5840,999],{"className":5841,"style":1151},[657,661,694],[568,5843,1533],{"className":5844},[657,661,694]," vergessen: ",[568,5847,5849,5893],{"className":5848},[571],[568,5850,5852],{"className":5851},[575],[577,5853,5854],{"xmlns":579},[581,5855,5856,5890],{},[584,5857,5858,5864,5866,5868,5870,5872,5874,5880,5882,5884],{},[587,5859,5860,5862],{},[590,5861,592],{},[596,5863,599],{"mathvariant":598,"lspace":618,"rspace":618},[596,5865,1519],{"stretchy":1518},[632,5867,634],{},[596,5869,1530],{"stretchy":1518},[596,5871,630],{},[590,5873,999],{},[980,5875,5876,5878],{},[590,5877,2348],{},[632,5879,989],{},[596,5881,604],{},[590,5883,1010],{},[980,5885,5886,5888],{},[590,5887,2348],{},[632,5889,884],{},[636,5891,5892],{"encoding":638},"y'(0) = \\alpha C_1 + \\omega C_2",[568,5894,5896,5952,6010],{"className":5895,"ariaHidden":644},[643],[568,5897,5899,5902,5934,5937,5940,5943,5946,5949],{"className":5898},[648],[568,5900],{"className":5901,"style":2616},[652],[568,5903,5905,5908],{"className":5904},[657],[568,5906,592],{"className":5907,"style":662},[657,661],[568,5909,5911],{"className":5910},[666],[568,5912,5914],{"className":5913},[670],[568,5915,5917],{"className":5916},[674],[568,5918,5920],{"className":5919,"style":679},[678],[568,5921,5922,5925],{"style":682},[568,5923],{"className":5924,"style":687},[686],[568,5926,5928],{"className":5927},[691,692,693,694],[568,5929,5931],{"className":5930},[657,694],[568,5932,599],{"className":5933},[657,694],[568,5935,1519],{"className":5936},[1215],[568,5938,634],{"className":5939},[657],[568,5941,1530],{"className":5942},[1281],[568,5944],{"className":5945,"style":787},[705],[568,5947,630],{"className":5948},[791],[568,5950],{"className":5951,"style":787},[705],[568,5953,5955,5958,5961,6001,6004,6007],{"className":5954},[648],[568,5956],{"className":5957,"style":2373},[652],[568,5959,999],{"className":5960,"style":1151},[657,661],[568,5962,5964,5967],{"className":5963},[657],[568,5965,2348],{"className":5966,"style":2380},[657,661],[568,5968,5970],{"className":5969},[666],[568,5971,5973,5993],{"className":5972},[670,1088],[568,5974,5976,5990],{"className":5975},[674],[568,5977,5979],{"className":5978,"style":1095},[678],[568,5980,5981,5984],{"style":2395},[568,5982],{"className":5983,"style":687},[686],[568,5985,5987],{"className":5986},[691,692,693,694],[568,5988,989],{"className":5989},[657,694],[568,5991,1122],{"className":5992},[1121],[568,5994,5996],{"className":5995},[674],[568,5997,5999],{"className":5998,"style":2414},[678],[568,6000],{},[568,6002],{"className":6003,"style":706},[705],[568,6005,604],{"className":6006},[710],[568,6008],{"className":6009,"style":706},[705],[568,6011,6013,6016,6019],{"className":6012},[648],[568,6014],{"className":6015,"style":2373},[652],[568,6017,1010],{"className":6018,"style":662},[657,661],[568,6020,6022,6025],{"className":6021},[657],[568,6023,2348],{"className":6024,"style":2380},[657,661],[568,6026,6028],{"className":6027},[666],[568,6029,6031,6051],{"className":6030},[670,1088],[568,6032,6034,6048],{"className":6033},[674],[568,6035,6037],{"className":6036,"style":1095},[678],[568,6038,6039,6042],{"style":2395},[568,6040],{"className":6041,"style":687},[686],[568,6043,6045],{"className":6044},[691,692,693,694],[568,6046,884],{"className":6047},[657,694],[568,6049,1122],{"className":6050},[1121],[568,6052,6054],{"className":6053},[674],[568,6055,6057],{"className":6056,"style":2414},[678],[568,6058],{},", nicht nur ",[568,6061,6063,6083],{"className":6062},[571],[568,6064,6066],{"className":6065},[575],[577,6067,6068],{"xmlns":579},[581,6069,6070,6080],{},[584,6071,6072,6074],{},[590,6073,1010],{},[980,6075,6076,6078],{},[590,6077,2348],{},[632,6079,884],{},[636,6081,6082],{"encoding":638},"\\omega C_2",[568,6084,6086],{"className":6085,"ariaHidden":644},[643],[568,6087,6089,6092,6095],{"className":6088},[648],[568,6090],{"className":6091,"style":2373},[652],[568,6093,1010],{"className":6094,"style":662},[657,661],[568,6096,6098,6101],{"className":6097},[657],[568,6099,2348],{"className":6100,"style":2380},[657,661],[568,6102,6104],{"className":6103},[666],[568,6105,6107,6127],{"className":6106},[670,1088],[568,6108,6110,6124],{"className":6109},[674],[568,6111,6113],{"className":6112,"style":1095},[678],[568,6114,6115,6118],{"style":2395},[568,6116],{"className":6117,"style":687},[686],[568,6119,6121],{"className":6120},[691,692,693,694],[568,6122,884],{"className":6123},[657,694],[568,6125,1122],{"className":6126},[1121],[568,6128,6130],{"className":6129},[674],[568,6131,6133],{"className":6132,"style":2414},[678],[568,6134],{},{"title":6136,"searchDepth":6137,"depth":6137,"links":6138},"",2,[6139,6140,6141],{"id":561,"depth":6137,"text":562},{"id":2661,"depth":6137,"text":2662},{"id":5062,"depth":6137,"text":5063},[6143,6145,6147,6149,6152,6154,6156,6158],{"lhs":6144,"rhs":634},"((u^2 - w^2)*cos(w*x) - 2*u*w*sin(w*x)) - 2*u*(u*cos(w*x) - w*sin(w*x)) + (u^2 + w^2)*cos(w*x)",{"lhs":6146,"rhs":634},"((u^2 - w^2)*sin(w*x) + 2*u*w*cos(w*x)) - 2*u*(u*sin(w*x) + w*cos(w*x)) + (u^2 + w^2)*sin(w*x)",{"lhs":6148,"rhs":634},"(-a\u002F2)^2 - (b - a^2\u002F4) + a*(-a\u002F2) + b",{"lhs":6150,"rhs":6151},"re((-2 + sqrt(4 - 20))\u002F2)","-1",{"lhs":6153,"rhs":884},"im((-2 + sqrt(4 - 20))\u002F2)",{"lhs":6155,"rhs":989},"-1 + 2*1",{"lhs":6157,"rhs":4635},"im(sqrt(-9))",{"lhs":6159,"rhs":634,"where":6160},"round((C1*cos(3*(x + 0.001)) + C2*sin(3*(x + 0.001)) - 2*(C1*cos(3*x) + C2*sin(3*x)) + C1*cos(3*(x - 0.001)) + C2*sin(3*(x - 0.001)))\u002F0.001^2 + 9*(C1*cos(3*x) + C2*sin(3*x)), 4)",{"C1":6161,"C2":6161,"x":6162},1,0.5,"y'' + a\\,y' + b\\,y = 0,\\ a^2 \u003C 4b,\\ \\alpha = -\\tfrac{a}{2},\\ \\omega = \\sqrt{b - \\tfrac{a^2}{4}}","\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 = 0,\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" 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class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\"><\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">4\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath 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