一阶非齐次线性微分方程通解的教学设计

Teaching Design for the General Solutions of First-Order Nonhomogeneous Linear Differential Equations

摘要: 针对一阶非齐次线性微分方程求通解时所用的常数变易法难于理解的问题，本文先利用类比和分离变量法解释常数变易法，以帮助学生更好地理解和掌握此部分内容；其次利用分组凑微分法又给出微分方程通解的一种求解思路和过程，以期开阔学生的求解思路，增强知识间的联系与融会贯通。

Abstract: To address the difficulty in understanding the method of variation of constants for the general solution of first-order nonhomogeneous linear differential equations, this paper first interprets the method of variation of constants by analogy and separation of variables to help students better understand and master this part. In addition, this paper presents another way using grouping differential method to broaden students’ thinking and promote the integration of relevant knowledge.