求解常系数线性微分方程 [tex=7.214x1.429]rjzw0bBUODiY66l+Mq83xAXwlAVED7uHGkHFCg7m+lX8E3suvLRzPfftKOPAIm+4Hq4gIYyxaAz3LuRirAOrHQ==[/tex]

2022-06-01

求解常系数线性微分方程 [tex=7.214x1.429]rjzw0bBUODiY66l+Mq83xAXwlAVED7uHGkHFCg7m+lX8E3suvLRzPfftKOPAIm+4Hq4gIYyxaAz3LuRirAOrHQ==[/tex]

答案：

解: 对应的齐次方程 [tex=4.143x1.357]rjzw0bBUODiY66l+Mq83xAXwlAVED7uHGkHFCg7m+lXlulU52+5YPU3mrCOVKtlN[/tex] 有特征值 [tex=2.214x1.214]wTNNLCLVN6eu2guGuMpHAg==[/tex] 及两重特征值 [tex=3.071x1.286]L65nP3yeOnJNB85hEgxbJk+bEpDfuwmIeX2BokbhzTY=[/tex] 通解为 [tex=6.929x1.214]GT/F6rZz91N79HpFdi1RgGaClkUzZKeAAARg7Gd3JUuKM/Hvo51nfBDnp6YS1fig[/tex] 常系数非齐次方程右端为多项式,对应于齐次方程二重零特征值, 即右端为 I 型 [tex=4.714x1.214]7OuOEhsW91tTsH8H77NSkQ==[/tex] 方程有多项式形式特解 [tex=9.071x1.571]O1+tQ4NSOxoMkeOswgbVKg3EUYwZ+UIKgsJ2mZqZuRHwZq3mbD49PsTyQjYrGMoa[/tex] 代入原方程有 [tex=27.714x1.429]rjzw0bBUODiY66l+Mq83xAXwlAVED7uHGkHFCg7m+lWDkLQBLItDcFfCD7V8QUCAqzR9Rwo1GlalfFuoAhdkDthv1L3Q31+WCze+zWslWMx1bqHcIh1uvgpSWvHDBMZ7aqaQ5aeZSOeQ+0A7F9HfPZZxehffYRnbQR7lfQkrffcORsOoVj4ExlFMIZGG4cwU[/tex]得 [tex=9.571x1.214]lgCz4WauHrYd8i/WDmabAWVi64JmP+BiyQg/z9FdguM=[/tex] 于是微分方程的通解为 [tex=12.857x1.429]GT/F6rZz91N79HpFdi1RgGaClkUzZKeAAARg7Gd3JUvMTfPri/WIs6r23fY9CAhbloyshBv6dtcrRP+tDvSD1w==[/tex].

举一反三

内容

0
求解下列常系数线性微分方程 : [tex=8.429x1.429]tRnrQWMhUlQy6Zihn7C/bF/4jIa0NmPn3uNAs5oxBDF+uDSpVFGiqJbcv1udjYZF[/tex]
1
【计算题】5 ×8= 6×4= 7×7= 9×5= 2×3= 9 ×2= 8×9= 7×8= 5×5= 4×3= 5+8= 6 ×6= 3×7= 4×8= 9×3= 1 ×2= 9×9= 6×8= 8×0= 4×7=
2
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3
求解常系数线性微分方程 : [tex=9.571x1.357]5N4fE/+TRNVJnPQE2QZxnl/pCbSVl7Hrof8ITZGc/CqwZRj7gl3iGwr7YlG3YUQkRAQIMc71frwIU4vx4IabWGJY6sY7yxReCOaFUAUe/Iw=[/tex]
4
>>>x= [10, 6, 0, 1, 7, 4, 3, 2, 8, 5, 9]>>>print(x.sort()) 语句运行结果正确的是( )。 A: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10] B: [10, 6, 0, 1, 7, 4, 3, 2, 8, 5, 9] C: [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0] D: ['2', '4', '0', '6', '10', '7', '8', '3', '9', '1', '5']