What Is the Correct Solution to the Differential Equation xy'^2 + yy' = 0?

[geft]

xy'^2 + yy' = 0 where y' = dy/dx

The answer is C1 = y and C2 = xy but I get this:

y'(xy' + y) = 0 where y' = 0 and thus y = C1

For the other solution:
xy' + y = 0
y' = -y/x
y = -y ln x + C2
C2 = y + y ln x

Full question is here: http://www.cramster.com/solution/solution/640396

 

[Mentallic]

y' = -y/x
y = -y ln x + C2

You can't take the antiderivative of that expression because y is a function of x but you've treated y as a constant.

Try get the x and dx on one side, and the y and dy on the other, then integrate.

 

[geft]

Ah, I see my mistake now. Thanks!