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

作　　者：范周田[1] 张汉林[1] FAN Zhou-tian;ZHANG Han-lin(College of Science,Beijing University of Technology,Beijing 100124,China)

机构地区：[1]北京工业大学应用数理学院,北京100124

出　　处：《大学数学》2018年第1期89-93,共5页College Mathematics

摘　　要：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.

关 键 词：常系数非齐次线性微分方程 变量替换 通解 特解 

分 类 号：O172.1[理学—数学]