Solve the initial value problem

$\displaystyle dy/dx=2y^2+xy^2$

I found the explicit solution to be:

$\displaystyle y=-1/(2x+x^2/2-1)$

and now the question is how do I attain its minimum. I know I'm supposed to take a derivative somewhere but I'm not sure of what. The answer is $\displaystyle x=-2$

I hate how I keep getting parts of every question but not a single entire question.