常数变易法求解微分方程研究  

Research on Solving Differential Equations by Constant Variation Method

作　　者：旷雨阳[1] 李兴华[1] 王太荣[1] KUANG Yu-yang;LI Xing-hua;WANG Tai-rong(Anshun University,Anshun 561000,China)

机构地区：[1]安顺学院,贵州安顺561000

出　　处：《扬州职业大学学报》2023年第3期47-50,共4页Journal of Yangzhou Polytechnic College

基　　金：贵州省科技计划项目(黔科合LH字〔2017〕7051)。

摘　　要：探讨常数变易法在解一阶线性微分方程、高阶线性微分方程及方程组中的应用,总结常数变易法求解各类微分方程的共同特点,推演出常数变易法的解题思路。通过典型例题,解析常数变易法解题实质内涵,概括常数变易法解题的一般方法。This paper discusses the application of constant variation method in solving the first-order linear differential equations,higher-order linear differential equations,and the systems of linear differential equations,summarizes the common features in those applications,and deduces the solving ideas of constant variation method.Through the explanation of typical examples,the essence of constant variation method is analyzed,and the general conclusion of constant variation method is summarized.

关 键 词：常数变易法 常微分方程 微分方程 通解 基解矩阵 

分 类 号：O175.1[理学—数学]