文档介绍：摘要本文首先介绍了恰当方程的定义及其充要条件, 然后对于非恰当方程引出积分因子的定义等基本概念和存在条件。鉴于积分因子的不唯一性和解题过程中的复杂性, 我们总结出几种特殊形式的积分因子, 并分析了多种方法来求解微分方程的中积分因子, 然后通过实例验证这些方法的有效性,最后运用这些方法求出四种基本类型方程的积分因子。关键词:恰当方程积分因子通解微分方程 Abstract This paper firstly introduces the definition and the necessary and sufficient conditions of exact equation, and then introduce the definition of integral factor and the existence conditions for the exact equation .Considering the no uniqueness of exact equation and plex of the process of solving, we summarized some special form of integral factor, and analyzes the various methods to solve integral factor of differential equations , then we shows the effectiveness of these methods through the example , finally we use these methods to work out integral factors of four basic types the equation. 目录一、恰当方程的定义和充要条件....................................................................... 1 二、积分因子的定义.................................................................................................. 1 三、积分因子的存在条件....................................................................................... 2 四、积分因子的形式.................................................................................................. 3 只与 x 有关的积分因子....................................................................................... 3 只与 y 有关的积分因子...................................................................................... 4 形为)(yxu?的积分因子................................................................................... 5 形为)(by axu?的积分因子................................................................................ 6 形为)( xyu 的积分因子........................................................................................ 8 形为)( 22yxu?的积分因子............................................................................. 10 形为)( bany mx u?的积分因子........................................................................ 12 形为)( ??yxu 的积分因子.........................................................