This equation was under the heading "separable equations" and I am supposed to solve it explicitly but I do not see how it is separable since the $\displaystyle x^{2}y$ term cannot be manipulated (in any way I can see) so as to only have functions M(x) and N(y) s.t. $\displaystyle M(x)+N(y)\frac{dy}{dx}=0$

$\displaystyle

\frac{dy}{dx}=\frac{2x}{y+(x^2)y}

$

where $\displaystyle y(0)=-2$

Any help would be much appreciated. Can $\displaystyle N(y)=y+x^{2}y$ and $\displaystyle M(x)=-2x$ where x is a constant in N(Y)? but that doesn't make sense because x is not a constant in the equation overall...