英语翻译本文着重讨论了一阶常微分方程的积分因子问题.首先,我们介绍了积分因子存在的充要条件,并进一步给出了一阶常微分方程

This article emphatically discussed the first-order differential equation of integral factor problems. First of all, we introduced the sufficient and necessary conditions for the existence of integral factor, and further gives a order ordinary differential equation with form if, special form of integral factor exist the sufficient and necessary condition. Finally, as application, we consider the integral factor in proof logarithmic formula and some inequalities, promotion application results of related literatures, enriching the differential equation solution.