常数变易法在微分方程求解中的应用探究  

Application of Constant Variation Method in the Solution of Differential Equations

作　　者：旷雨阳[1] 李兴华[1] 王太荣[1] KUANG Yu-yang;LI Xing-hua;WANG Tai-rong(Department of Mathematics and Computer,Anshun College,Anshun 56100,China)

机构地区：[1]贵州省安顺学院数计学院,贵州安顺561000

出　　处：《南通职业大学学报》2023年第2期73-75,共3页Journal of Nantong Vocational University

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,是拉格朗日历经十一年研究的一种特殊的变量代换法。为探究常数变易法的教学拓展,将常数变易法应用于求解线性微分方程组和高阶线性微分方程,通过常数变易过程,给出简洁推演,建立通解公式,并以典型示例,阐明了公式的实际操作过程。Constant variation is an effective method for solving ordinary differential equations.It is a special variable substitution method worked out by Lagrange over 11-year research.For the pedagogical expansion of constant variation method,the constant variation method is applied to the solving system of linear differential equations and higher order linear differential equations.In the process of constant variation,a concise and clear deduction is given to establish the effective general solution formula,and the practical operation of formula is illustrated with the typical examples.

关 键 词：常数变易法 线性微分方程组 基解矩阵 高阶线性微分方程 通解 

分 类 号：O175[理学—数学]