求常微分方程积分因子的一般方法

The General Methods for Solving Integrating Factors of Ordinary Differential Equations

给出了一阶常微分方程P(x,y)dx+Q(x,y)dy=0具有形如μ=μ(φ(x,y))的积分因子的充要条件,同时也考虑了一些常见特殊形式,如形为μ=((fx)+h(y))和μ((fx)*h(y))等,并将之应用于实例。

This paper discusses the problem of integral factor for the first ordinary differential equationP（x,y）dx＋Q（x,y）dy=0,and gives a sufficient and necessary condition of integral factor with the form of μ=μ（φ（x,y））.Moreover,the paper discusss some special forms integral factors such as μ（f（x）＋h（y））and μ（f（x）＊h（y））.At last,the paper applies the methods to some examples.