\[ y'(x)=F\left (y(x)-x^2\right )+2 x \] ✓ Mathematica : cpu = 0.161354 (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 = 0.12 (sec), leaf count = 22
\[ \left \{ y \left ( x \right ) ={x}^{2}+{\it RootOf} \left ( -x+\int ^{{\it \_Z}}\! \left ( F \left ( {\it \_a} \right ) \right ) ^{-1}{d{\it \_a}}+{\it \_C1} \right ) \right \} \]