高阶常系数齐次线性微分方程的解法

High Order Constant Coefficient Linear Differential Equation Solution

常微分方程是微积分学的重要组成部分,求解高阶微分方程是常微分方程的一难点问题,通常用适当的变量代换,达到降阶的目的来解决问题。结合多年的教学经验,归纳总结给出高阶常系数齐次线性微分方程的一些求解方法,包括常系数齐次线性微分方程和欧拉方程以及可降阶的高阶微分方程等,并通过例题阐述各种方法。

Ordinary Differential equation is an important part of differential and integration. Solving Ordinary Differential equation of difficult prob- lem is the differential equations of high order. Generally, in order to achieve the purpose to solve problems, it uses an appropriate variable substitution. With many years of teaching experience, summarizes to give some methods for solving the linear differential equation of higher-order, including homogeneous linear differential equation with constant coefficient, Euler equations and higher-order differential of reduce order and so on, gives an example to explain a variety of methods.