| n阶变系数线性常微分方程的可积性 |
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| 引用本文： | 胡爱莲,郭俊.n阶变系数线性常微分方程的可积性[J].喀什师范学院学报,2009,30(6):3-6,17. |
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| 作者姓名： | 胡爱莲 郭俊 |
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| 作者单位： | 喀什师范学院数学系,新疆,喀什,844007 |
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| 摘 要： | 讨论了一类四阶、五阶变系数线性常微分方程的可积性，进而给出了方程y^（n）＋a1（x）y^（n-1）＋a2（x）y^（n-2）＋…＋an-1（x）y＇＋an（x）y=F（x）在条件{ana2＋ana＇1-a1a＇n=0 ana3＋ana＇2-a2a＇n=0 … … … anan-1＋ana＇n-2-an-1a＇n=0 a^2n＋ana＇n-1-an-1a＇n=0下的初等积分法，并推出了其求解公式．
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| 关 键 词： | 变系数线性非齐次微分方程 初等积分法 通解 |
The Integrability of the n-order Variable Coefficients Linear Ordinary Differential Equation |
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| HU Ai-lian,GUO Jun.The Integrability of the n-order Variable Coefficients Linear Ordinary Differential Equation[J].Journal of Kashgar Teachers College,2009,30(6):3-6,17. |
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| Authors: | HU Ai-lian GUO Jun |
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| Institution: | HU Ai-lian,GUO Jun (The Department of Mathematics,Kashgar Teachers College,Kashgar 844007,Xinjiang) |
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| Abstract: | Abstract：This paper considers the integrability of the class of fourth-order variable coefficient non-homogeneous linear differential equation, and deduces the integrability of the following equation and gives its the general solution formulas：y^（n）＋a1（x）y^（n-1）＋a2（x）y^（n-2）＋…＋an-1（x）y＇＋an（x）y=F（x）when the following conditions are satisfied {ana2＋ana＇1-a1a＇n=0 ana3＋ana＇2-a2a＇n=0 … … … anan-1＋ana＇n-2-an-1a＇n=0 a^2n＋ana＇n-1-an-1a＇n=0 |
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| Keywords: | Variable coefficient non-homogeneous linear differential equation Integrability General solution Elementary integral method |
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