求通解:(xy-x^2)dy=y^2dx
问题描述：
求通解:(xy-x^2)dy=y^2dx
答
(xy-x^2)dy=y^2dx
dy/dx=y^2/(xy-x^2)
令y/x=t y=xt
dy=/dx=t+xdt/dx
t+xdt/dx=t^2/(t-1)
xdt/dx=t/(t-1)
(1-1/t)dt=dx/x
t-lnt=lnx +c
y/x-ln(y/x)=lnx+c