IVP ODE checking specifics of solution

[cambo86]

Homework Statement

I've got an IVP where,
3xy+y²+(x²+xy)y'=0, y(1)=0

The Attempt at a Solution

I've solved to get,
x²y(x+\frac{1}{2}y)=0

Is it correct to say,
x=0 or y=0 or y=-2x,
Since y= 0 is the only solution that fits y(1)=0, then
y=0 \forallx

 

[LCKurtz]

I didn't check your solution. But in any case, x=0 wouldn't be a solution. Otherwise, assuming your work is OK, yes.