常数变易法教学研究

Teaching Research on Constant Variation Method

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.