一阶微分方程三类积分因子的计算

Three Integrating Factors of First Order Differential Equation

给出了一阶微分方程M (x ,y)dx +N(x ,y)dy =0 ,具有1.μ(x ,y) =F(ax +by) , 2 .μ(x ,y) =G(xy) ,3.μ(x ,y) =exp[∫f(x)dx +∫g(y)

We shall show sufficient and necessary condition that first order differential equation M(x,y)dx+N(x,y)dy=0 have 1,μ(x,y)=F(ax+by),2,μ(x,y)-G(xy), 3,μ(x,y)=exp[∫f(x)dx+∫g(y)dy] three forms integrating factors.