yf(xy)dx+xg(xy)dy=0即f(xy)y+g(xy)xy'=0令v=xy，则有v'=y+xy'代入可得：f(v)y+g(v)(v'-y)=0即[f(v)-g(v)]y+g(v)v'=0两边同时乘以xdx得：[f(v)-g(v)]vdx+g(v)xdv=0分离变量得：dx/x=g(v)/v[g(v)-f(v)]dv积分可得：ln|x|+A=∫g(v)/v[g(v)-f(v)]dv不妨设F(v)=∫g(v)/v[g(v)-f(v)]dv可得：F(v)=ln|x|+A解得：v=G(x)即y=G(x)/x是为通解。这里关键是积分的运算，除此之外就是F(v)的
反函数G(x)的运算。