Question

Solve y'=y/(y-2x) implicitly.

Answer 1

@aaronq @abb0t @ParthKohli

Answer 2

substitute `y = ux`

Answer 3

y=ux
u=y/x
y'=u+u'x
u'x+u=ux/(ux-2x)=u/(u-2)
u'x=u/(u-2)-u=u/(u-2)-(u(u-2))/(u-2)
=(u-u^2+2u)/(u-2)=(3u-u^2)/(u-2)=(u(3-u))/(u-2)

Answer 4

yes separate variables and do partial fractions

Answer 5

I don't know why the answer in the book is y^2(y-3x)=C when I got
y^2(3x-y)=C as the answer. Am I right?

Answer 6

I see why. I think it's because of the constant C. Since C can be both positive and negative because it's constant.