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 (eN/ex-eM/ey)/(2yM-2xN)=f(x2+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((δ)N/(δ)x-(δ)M/(δ)y)/(2yM - 2xN) =f(x2 + y2) are showed.
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