一道二阶线性微分方程题目的多种解法及思想方法的意义

Multiple Solutions to a Second-Order Linear Differential Equation Problem and the Significance of the Thinking Methods

摘要: 文章以一道二阶线性微分方程为例，归纳出六种不同的解题方法，分别是常数变易法、微分算子法、Laplace变换、配凑法、待定系数法、程序法，并进一步阐述微分方程的一题多解，有利于学生搭建完整的知识体系结构，从多个角度体会解题方法和技巧，提高学生的发散思维和创新能力。

Abstract: Taking a second-order linear differential equation as an example, this paper summarizes six different problem-solving methods, namely the method of variation of constants, the differential operator method, the Laplace transform method, the method of assembling and matching, the method of undetermined coefficients, and the programming method. Furthermore, it elaborates that multiple solutions to one differential equation problem are beneficial for students to build a complete knowledge system structure, experience problem-solving methods and techniques from multiple perspectives, and improve students’ divergent thinking and innovative abilities.