关于一阶线性微分方程解法的一个注记

A Note on Solving Linear Differential Equation of the First-order

常数变易法是求解一阶线性微分方程的有效方法,但在求解某些微分方程时其过程比较繁琐。为了简化求解运算过程,给出了解一阶线性微分方程y′+p(x)y=q(x)的一种新思路,即将常数变易法公式y=C(x)e-∫p(x)dx设为y=e-∫p(x)dx(u(x)+C),这里u(x)是满足u′(x)e-∫p(x)dx=q(x)的待定函数,C为任意常数。

Constant variation is an effective method for linear differential equation of the iirst-order. However, in order to simplify the solving process,a new solution for a linear differential equations y＇ ＋p （x）y=q （x） is presented. That is, take y=C（x）e-fP（x）dx by y=e-fP（x）dx（u（x）＋C）, where u（x） satisfies and C is arbitrary constant.