常系数非齐次线性微分方程的变量替换法

Method of Variable Substitution to Solve the Non Homogeneous Lineal Differential Equation with Constant Coefficients

常系数非齐次线性微分方程求解是微积分教学的一个难点,主要困难是特解形式复杂和计算量大.本文用变量替换的思想研究这类微分方程的特解,从最简单的情形出发,通过类比得出复杂情形下方程的解法.使用变量替换把复杂问题简单化,求解不需要特解形式,有效降低了计算量.

Solving non homogeneous lineal differential equation with constant coefficients is a difficult point in the process of teaching,the main difficult are both complexity of special solution’s form and large amount of calculation.This paper,from the simple situation,give a method through analogy and simplify the complexityproblem through variable substitution.The method does not need the forms of the special solutions,which great reduced the amount of calculation.