\[ y'(x)=F\left (y(x)-x^2\right )+2 x \] ✓ Mathematica : cpu = 0.187151 (sec), leaf count = 100
\[\text {Solve}\left [\int _1^{y(x)}-\frac {F\left (K[2]-x^2\right ) \int _1^x-\frac {2 K[1] F'\left (K[2]-K[1]^2\right )}{F\left (K[2]-K[1]^2\right )^2}dK[1]+1}{F\left (K[2]-x^2\right )}dK[2]+\int _1^x\left (\frac {2 K[1]}{F\left (y(x)-K[1]^2\right )}+1\right )dK[1]=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.054 (sec), leaf count = 22
\[y \relax (x ) = x^{2}+\RootOf \left (-x +\int _{}^{\textit {\_Z}}\frac {1}{F \left (\textit {\_a} \right )}d \textit {\_a} +c_{1}\right )\]