高阶线性微分方程解法探讨  

The Solution of Higher Order Linear Differential Equation

作　　者：张莹[1] 赵伟[1] ZHANG Ying;ZHAO Wei(Zhengzhou Railway Vocational and Technical College, Zhengzhou 451460, China)

机构地区：[1]郑州铁路职业技术学院,河南郑州451460

出　　处：《郑州铁路职业技术学院学报》2020年第4期32-36,共5页Journal of Zhengzhou Railway Vocational and Technical College

摘　　要：介绍高阶微分方程的理论与结构,研究高阶齐次和非齐次线性微分方程的求解方法,在解齐次线性微分方程中主要采用欧拉待定指数函数法(又称为特征根法),在求解非齐次线性微分方程中主要采用常数变易法、比较系数法、拉普拉斯变换法。In this paper,the theory and structure of higher order differential equation are firstly introduced,followed by the solution of high order homogeneous linear differential equation and the method of solving high order nonhomogeneous linear differential equation.In solving the homogeneous linear differential equation,the Eulerian exponential function method(also called the eigenvalue method)is used.In the non-homogeneous linear differential equation,the constant method,the comparison coefficient method,the Laplace transform method are mainly used.

关 键 词：高阶微分方程 特征根法 常数变异法 

分 类 号：O13[理学—数学]