\[ y'(x)=\frac {1}{2} e^{\frac {x^2}{4}} \left (2 F\left (e^{-\frac {x^2}{4}} y(x)\right )+e^{-\frac {x^2}{4}} x y(x)\right ) \] ✓ Mathematica : cpu = 60.227 (sec), leaf count = 169
\[\text {Solve}\left [c_1=\int _1^{y(x)} \left (-\int _1^x \frac {e^{-\frac {1}{2} K[1]^2} K[1] \left (e^{\frac {K[1]^2}{4}} F\left (e^{-\frac {1}{4} K[1]^2} K[2]\right )-K[2] F'\left (e^{-\frac {1}{4} K[1]^2} K[2]\right )\right )}{2 F\left (e^{-\frac {1}{4} K[1]^2} K[2]\right )^2} \, dK[1]-\frac {e^{-\frac {x^2}{4}}}{F\left (e^{-\frac {x^2}{4}} K[2]\right )}\right ) \, dK[2]+\int _1^x \left (\frac {y(x) e^{-\frac {1}{4} K[1]^2} K[1]}{2 F\left (y(x) e^{-\frac {1}{4} K[1]^2}\right )}+1\right ) \, dK[1],y(x)\right ]\]
✓ Maple : cpu = 0.155 (sec), leaf count = 27
\[ \left \{ y \left ( x \right ) ={{\it RootOf} \left ( -x+\int ^{{\it \_Z}}\! \left ( F \left ( {\it \_a} \right ) \right ) ^{-1}{d{\it \_a}}+{\it \_C1} \right ) \left ( {{\rm e}^{-{\frac {{x}^{2}}{4}}}} \right ) ^{-1}} \right \} \]