\[ y'(x)=-x \left (-F\left (y(x)-\frac {1}{2} e^{-x^2} x^2\right )+e^{-x^2} x^2-e^{-x^2}\right ) \] ✓ Mathematica : cpu = 77.145 (sec), leaf count = 358
\[\text {Solve}\left [\int _1^{y(x)} -\frac {F\left (K[2]-\frac {1}{2} e^{-x^2} x^2\right ) \int _1^x \left (\frac {e^{-K[1]^2} K[1]^3 F'\left (K[2]-\frac {1}{2} e^{-K[1]^2} K[1]^2\right )}{F\left (K[2]-\frac {1}{2} e^{-K[1]^2} K[1]^2\right )^2}-\frac {e^{-K[1]^2} K[1] \left (e^{K[1]^2} F\left (K[2]-\frac {1}{2} e^{-K[1]^2} K[1]^2\right )+1\right ) F'\left (K[2]-\frac {1}{2} e^{-K[1]^2} K[1]^2\right )}{F\left (K[2]-\frac {1}{2} e^{-K[1]^2} K[1]^2\right )^2}+\frac {K[1] F'\left (K[2]-\frac {1}{2} e^{-K[1]^2} K[1]^2\right )}{F\left (K[2]-\frac {1}{2} e^{-K[1]^2} K[1]^2\right )}\right ) \, dK[1]+1}{F\left (K[2]-\frac {1}{2} e^{-x^2} x^2\right )} \, dK[2]+\int _1^x \left (\frac {e^{-K[1]^2} K[1] \left (e^{K[1]^2} F\left (y(x)-\frac {1}{2} e^{-K[1]^2} K[1]^2\right )+1\right )}{F\left (y(x)-\frac {1}{2} e^{-K[1]^2} K[1]^2\right )}-\frac {e^{-K[1]^2} K[1]^3}{F\left (y(x)-\frac {1}{2} e^{-K[1]^2} K[1]^2\right )}\right ) \, dK[1]=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.872 (sec), leaf count = 34
\[ \left \{ y \left ( x \right ) ={\frac {{x}^{2}{{\rm e}^{-{x}^{2}}}}{2}}+{\it RootOf} \left ( {x}^{2}-2\,\int ^{{\it \_Z}}\! \left ( F \left ( {\it \_a} \right ) \right ) ^{-1}{d{\it \_a}}+2\,{\it \_C1} \right ) \right \} \]