由一道习题引发的反思

Reflection On a Problem

常系数变易法是求解一阶线性微分方程的常规解法.步骤是先求齐次方程的通解,再将通解中的C换做C(x),设为方程的通解,代入原方程,求出C(x),从而求出原方程的通解.学生在课后一道习题的解答中出现了非常规的解法,通过对这些解法分析和总结,可以拓宽学生的解题思路,提高学生探究问题的热情和学习高等数学的积极性,培养和发展学生的思维能力.

Constant variation method is the conventional solution to the first-order linear differential equation.The first step is the general solution of homogeneous equation,then C in the general solution is replaced by C(x)which is set to the general solution of equation,and C(x)is obtained.The general solution of the original equation is thus obtained.The students found unconventional solutions in the solution to an exercise after class.The analysis and summary of these solutions can broaden students'thinking of solving problems,improve students’enthusiasm for exploring problems and enthusiasm for learning higher mathematics,and cultivate and develop students’thinking ability.