(dy/dx)^3-4xy(dy/dx)+8y^2=0求通解

解：设y'=p
则代入原方程得 p³-4xyp+8y²=0
==>x=p²/4y+2y/p.........(1)
令f(y,p)=p²/4y+2y/p
∵f'y=-p²/(4y