求微分方程y^3 dx -(1-2xy^2)dy=0的通解.

y^3dx-(1-2xy^2)dy=0
y^3dx+2xy^2dy=dy
y^2dx+2xydy=dy/y
y^2dx+xdy^2=dy/y
d(xy^2)=dlny
通解xy^2=lny+C