## 二阶变系数微分方程求解方法的研究

Studying on the Solving Method of the SecondOrder
Differential Equationwith Variable Coefficients
Abstract:This paper is pided into three parts to discuss the solution of second order variable coefficient differential equation, first of all, construction method by the use of specific index function to solve the second order variable coefficient linear homogeneous differential equation, the second use of degradation, constant variation, tectonic progression method to solve the nonhomogeneous differential equation, the last discuss the problem of second order nonlinear differential equation with variable coefficients.
Key words:Liouville formula;Constructor;Constant variation method;The general solution; Special solution

1.二阶变系数齐次线性微分方程解的求法    3
1.1常数变易法    3
1.2特定指数函数法    4
1.3构造法    4
2.二阶变系数非齐次微分方程解的求法    8
2.1降阶法    8
2.2常数变易法    10
2.3构造级数解    12
3.一类二阶变系数非线性微分方程的通解    15

本文在前人研究的基础之上,又查阅了大量的文献、参考资料以及相关二阶变系数线性微分方程的著作和教材,最后通过对微分方程理论的深入研究,将方程分为三部分来讨论.首先讨论二阶变系数线性齐次微分方程,其次研究非齐次线性微分方程,最后讨论一类二阶变系数非线性微分方程的问题.
1.二阶变系数齐次线性微分方程解的求法

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