\[ y'(x)=x \left (F\left (y(x)-\frac {1}{2} e^{-x^2} x^2\right )-e^{-x^2} x^2+e^{-x^2}\right ) \] ✓ Mathematica : cpu = 0.603505 (sec), leaf count = 361
\[\text {Solve}\left [\int _1^{y(x)}-\frac {F\left (K[2]-\frac {1}{2} e^{-x^2} x^2\right ) \int _1^x\left (\frac {e^{-K[1]^2} F'\left (K[2]-\frac {1}{2} e^{-K[1]^2} K[1]^2\right ) K[1]^3}{F\left (K[2]-\frac {1}{2} e^{-K[1]^2} K[1]^2\right )^2}-\frac {e^{-K[1]^2} \left (e^{K[1]^2} F\left (K[2]-\frac {1}{2} e^{-K[1]^2} K[1]^2\right )+1\right ) F'\left (K[2]-\frac {1}{2} e^{-K[1]^2} K[1]^2\right ) K[1]}{F\left (K[2]-\frac {1}{2} e^{-K[1]^2} K[1]^2\right )^2}+\frac {F'\left (K[2]-\frac {1}{2} e^{-K[1]^2} K[1]^2\right ) K[1]}{F\left (K[2]-\frac {1}{2} e^{-K[1]^2} K[1]^2\right )}\right )dK[1]+1}{F\left (K[2]-\frac {1}{2} e^{-x^2} x^2\right )}dK[2]+\int _1^x\left (\frac {e^{-K[1]^2} \left (e^{K[1]^2} F\left (y(x)-\frac {1}{2} e^{-K[1]^2} K[1]^2\right )+1\right ) K[1]}{F\left (y(x)-\frac {1}{2} e^{-K[1]^2} K[1]^2\right )}-\frac {e^{-K[1]^2} K[1]^3}{F\left (y(x)-\frac {1}{2} e^{-K[1]^2} K[1]^2\right )}\right )dK[1]=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.679 (sec), leaf count = 34
\[y \relax (x ) = \frac {x^{2} {\mathrm e}^{-x^{2}}}{2}+\RootOf \left (x^{2}-2 \left (\int _{}^{\textit {\_Z}}\frac {1}{F \left (\textit {\_a} \right )}d \textit {\_a} \right )+2 c_{1}\right )\]