一阶线性非齐次微分方程的解法探析

On the Solution to the First-order Linear Non-homogeneous Differential Equations

介绍求解一阶线性非齐次微分方程的积分变换法和积分因子法,有助于解决学生学习"常数变易法"中的存疑;通过对三种解法的辨析,明确各种解法的特点与关系;对同一问题,注重采用一题多解的教学方式,从不同角度、采用不同方法加以探究求解,有利于拓宽学生的解题思路,培养学生灵活解题的能力。

An introduction to the integral transform method and the integral factor method to solve the first-or- der linear inhomogeneous differential equation will help to solve the students＇ doubts in learning ＂the method of constant variation.＂ Through differentiating three solutions, each one has been made clear. To the same problem, dif- ferent solutions are provided so that the problem can be studied and solved from different angles and with different methods, which is helpful to broaden the students＇ problem-solving approaches and thus cultivate their ability to solve problems flexibly.