xy'-y=y^3
xdy/dx=y+y^3
dy/(y+y^3)=dx/x
dy/[y(1+y^2]=dx/x
d(y^2)/[y^2(1+y^2)]=2dx/x
d(y^2)*[1/y^2-1/(1+y^2)]=2dx/x
积分得:lny^2-ln(1+y^2)=2ln|x|+C1
y^2/(1+y^2)=Cx^2
d(y^2)/[y^2(1+y^2)]=2dx/x这步我看不懂,能不再解释呀
dy/[y(1+y^2]=dx/x,dy*y/[y^2(1+y^2)]=dx/xdy*2y/[y^2(1+y^2)]=2dx/xd(y^2)/[y^2(1+y^2)]=2dx/xd(y^2)*[1/y^2-1/(1+y^2)]=2dx/x