用幂级数解法求解方程 [tex=6.071x1.429]7/NebOJ+accrjPN+Co+D9eABCZdXJA+HGPdiTwzfWgQ=[/tex]

2022-05-26

用幂级数解法求解方程 [tex=6.071x1.429]7/NebOJ+accrjPN+Co+D9eABCZdXJA+HGPdiTwzfWgQ=[/tex]

答案：

解: 方程化为 [tex=5.571x2.214]uDURn6KTVSzuxHB9PQPJUth43arObYlIuKJqFbFu61RvrsDdfcpXllnniBOpdmPq[/tex] 因 [tex=9.357x2.571]vNUanqu6Pif/Ki305Ue94oVzvGn7I0x1zWgESmFoa/Zo61NfYQP2L1IGNGBADSdh[/tex]  故存在幂级数解. 设 [tex=13.857x1.429]aerGRP+gwFI+HG9F+qjMqgwOV3MCvKqTtvCiboYT+IMYfpBWnudPZ1XmZBVUv2LbjgTZGB/YduAeHvn/KAV5ZA==[/tex]将 [tex=3.286x1.357]rE7qcJ9vPU7NzJ3dD6qkEGio2FmU9GX6byJZN4X6dsyzn6LX+gqE50BROEKH2Rv+[/tex] 的表达式代入原方程,比较同次幂系数, 可得[tex=18.357x2.643]2T1DVDuqMwVTWjryg0nsUiyNzUOrAuENA7gcpp62v6WtPfntJbKQNmmZNx6k5fgUgEW9QWLYHpHn4Z8QxnL3/rbAbrXPZw0I8hWElBGYrIkMHJN4GOQ1IF0qp+V27Pz2HRWDXBrtAMQbWpYsljkcoQ==[/tex]考虑方程的通解, 可设 [tex=7.786x1.429]L7OjZMrHBWIzFbeMBOA8BYCwprK3fpxQkA2LRw8aLSLrJyAHMjBV0Tr0OjwfDt/1[/tex] 有 [tex=5.643x1.0]gw3QJyvIBNucufbaRv7zFNvwYYxYOvX8Spm+rB1S8ME=[/tex] [tex=4.571x2.357]sJvBnY8itVZPKHDO55V9RYqkb7iuNOdCgLVLDYw8B9s=[/tex] [tex=7.786x2.357]/7ESlLDrHrnBeqY7yzt69GuFTbPEKoMVyXsQLA554wXefLUtH60EW4YUXjJ7LAL0[/tex] [tex=15.5x2.714]gvZsY66Q34rELg+I2PYMPtN8xdspuHv5pgchI5iEwVDP3FFdmpLdvWT/Q/v4FmgKrTbCI6TLn7CRQCLRTW2ENQ==[/tex]于是可逐次递推求得幂级数解[tex=38.286x2.786]sWqSdPB6BFJuV7IJaMDm7Dohbk2aqLwJ76zs0aTrY0UowidX4Efsz2i4AKTUG3K0WfvgCuZNnfleNBza/slJ6wcVo05zBb6EIa74hsCnXgo60Dv2null211Nnk/Pl8K20loLdxPiNcOQ/Sy7XvLm2M0GWRKpAJk3jaNU+LwtQoTXh/zg8mYxKUrW62CXxQHegMJ7FLaHzjJyEx1ggfr0MXn5Qg6EcSJLBnBPVMi+2C6pumTrqKQKTkRHDBFQLYtXGKv0UXyNEGDxj/rjDwm6+9vVKU0HVqHqN548GbielLUSb1wzo3jSJEWLYX7v15T5JgAeZ90GAq3ku7EUAmKglQ==[/tex]

举一反三

内容

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