线性微分方程的解法探析  

Study on the Solution of Linear Differential Equation

作　　者：李秀琴[1] 宋国华[1] 

机构地区：[1]北京建筑工程学院基础科学部,北京100044

出　　处：《北京建筑工程学院学报》2006年第3期51-53,共3页Journal of Beijing Institute of Civil Engineering and Architecture

基　　金：北京市教育委员会科技发展计划面上项目(KM200410016010);北京市委组织部优秀人才资助项目(2004D0501704)

摘　　要：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.

关 键 词：齐线性微分方程 非齐线性微分方程 常数变易法 

分 类 号：O241.81[理学—计算数学]