\[ y'(x)=F\left (y(x)-x^2\right )+2 x \] ✓ Mathematica : cpu = 22.4081 (sec), leaf count = 88
\[\text {Solve}\left [c_1=\int _1^{y(x)} \left (-\int _1^x -\frac {2 K[1] F'\left (K[2]-K[1]^2\right )}{F\left (K[2]-K[1]^2\right )^2} \, dK[1]-\frac {1}{F\left (K[2]-x^2\right )}\right ) \, dK[2]+\int _1^x \left (\frac {2 K[1]}{F\left (y(x)-K[1]^2\right )}+1\right ) \, dK[1],y(x)\right ]\]
✓ Maple : cpu = 0.137 (sec), leaf count = 22
\[ \left \{ y \left ( x \right ) ={x}^{2}+{\it RootOf} \left ( -x+\int ^{{\it \_Z}}\! \left ( F \left ( {\it \_a} \right ) \right ) ^{-1}{d{\it \_a}}+{\it \_C1} \right ) \right \} \]