常数变易法教学研究  

Teaching Research on 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(College of Mathematics and Computer,Anshun University,Anshun,Guizhou 561000,China)

机构地区：[1]贵州省安顺学院数计学院,贵州安顺561000

出　　处：《杨凌职业技术学院学报》2023年第2期15-19,共5页Journal of Yangling Vocational & Technical College

基　　金：贵州省科技计划项目(黔科合LH字[2017]7051号)。

摘　　要：常数变易法是解常微分方程行之有效的一种方法,它是拉格朗日十一年的研究成果,是一种特殊的变量代换法。本文对常数变易法在求解一阶线性微分方程、高阶线性微分方程及其线性微分方程组进行相关研究,探讨出常数变易法在求解各类微分方程过程中的共同特点,从而揭示了常数变易法解题实质内涵,得出了常数变易法教学总结,概括了常数变易法解题的一般结论。The constant variation method is an effective method to solve ordinary differential equations.It is the research achievement of Lagrange in the past 11 years and a special variable substitution method.This paper studies the constant variation method in solving first-order linear differential equations,high-order linear differential equations and their linear differential equations,and discusses the common characteristics of constant variation method in solving various differential equations,Thus,the essence of constant variation method is revealed,the teaching summary of constant variation method is obtained,and the general conclusion of constant variation method is summarized.

关 键 词：常微分方程 常数变易法 通解 特解 基解矩阵 教学研究 

分 类 号：O175[理学—数学]