求方程dy/dx=y/(x-y^2)的通解

求方程dy/dx=y/(x-y^2)的通解
求方程dy/dx=y/(x-y^2)的通解

求方程dy/dx=y/(x-y^2)的通解
dx/dy=(x-y^2)/y=x/y-y
令x/y=p
x=py
dx/dy=dp/dy*y+p
代入得
dp/dy*y+p=p-y
dp=-dy
两边积分得
p=-y+C
x/y=-y+C