关于某些积分因子的存在条件

The existence condition for some types of integrating factor

积分因子方法是求解常微分方程的一种常用的方法.但目前常微分方程的教材中仅讨论了一些非常简单的积分因子的求解方法.介绍两种形式的积分因子的存在条件及其一些应用,这两种积分因子不但可适用于更一般的常微分方程,而且也使教材已求解的积分因子成为本文的特例.

In the problem of solving ordinary differential equation, using integrating factor is a useful method. But texts in ordinary differential equation only give some so simple equation that it can be solved by using integrating factor. This article will give two types of integrating factor： u （ x^ny^β）, u （ ax^m ＋ by^n ）, obtain the existence conditions, and apply these resnlts for solving more complicated ordinary equation whose resnlts are more general than these in the texts.