求(y^2-6x)dy/dx+2y=0的通解

(y^2-2x)dy/dx+2y=0
dy/dx=-2y/(y^2-2x)
dx/dy=(y^2-2x)/(-2y)
dx/dy=-y/2+x/y
x/y=u
dx=ydu+udy
ydu/dy+u=-y/2+u
ydu/dy=-y/2
du/dy=-1/2
u=-y/2+C0
通解x=-y^2/2+C0y
dx/dy=-y+C0,
(y^2-2x)/(-2y)=-y/2+x/y=-y+C0
书上答案:x=y^2/6+C/y
dx/dy=y/3-C/y^2
y^2-2x=y^2-y^2/3-2C/y=2y^2/3-2C/y
(y^2-2x)/(-2y)=-y/3+C/y^2
如果题目是:(y^2-2x)dy/dx-2y=0
dy/dx=2y/(y^2-2x)
dx/dy=(y^2-2x)/2y=y/2-x/y
ydx/dy=y^2/2-x
ydx/dy+x=y^2/2
dxy/dy=y^2/2
dxy=y^2dy/2
xy=y^3/6+C
x=y^2/6+C/y