一类积分因子存在的充要条件

The Sufficient and Necessary Condition of an Integrating Factors

根据全微分方程及积分因子的定义,给出了一阶微分方程M(x,y)dx+N(x,y)dy=0具有μ(x,y)=F(x2+y2)形式的积分因子的充要条件是(N/x)-(M/y)2yM-2xN=(fx2+y2)。

By the definition of complete differential equation and Integral factor,the sufficient and necessary condition of first order differential equation M（x,y）dx＋N（x,y）dy=0 have μ（x,y）=F（x2＋y2） form integrating factors is （δN/δx）-（δM/δy）2yM-2xN=（fx2＋y2） are showed.