线性微分方程的解法探析

Study on the Solution of Linear Differential Equation

常数变易法是求解非齐线性微分方程(组)的一种重要方法.首先求出非齐线性微分方程对应的齐线性微分方程(组)的通解,通过将通解中的任意常数变易为待定函数而求得非齐线性微分方程(组)的解.利用隐式解对常数变易法的思想来源进行分析,常数变易法的实质仍是一种变量变换方法.

Method of substitution of constants is an important method for solving nonhomogeneous linear differential equations. To get the solution of nonhomogeneous linear differential equations, firstly the corresponding homogeneous linear differential equations are solved, then to change the arbitrary constants of the general solution of the homogeneous linear differential equation into an undetermined function. In this paper, the train of thought of method of substitution of constants is analysed, and it is showed that method of substitution of constants is a method of change of variable indeed.