\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) =1/2\, \left ( y \left ( x \right ) {{\rm e}^{-1/4\,{x}^{2}}}x+2\,F \left ( y \left ( x \right ) {{\rm e}^{-1/4\,{x}^{2}}} \right ) \right ) {{\rm e}^{1/4\,{x}^{2}}}=0} \]
Mathematica: cpu = 49.253254 (sec), leaf count = 196 \[ \text {Solve}\left [\int _1^{y(x)} -\frac {e^{-\frac {x^2}{4}} \left (e^{\frac {x^2}{4}} F\left (e^{-\frac {x^2}{4}} K[2]\right ) \int _1^x \left (\frac {e^{-\frac {1}{4} K[1]^2} K[1]}{2 F\left (e^{-\frac {1}{4} K[1]^2} K[2]\right )}-\frac {e^{-\frac {1}{2} K[1]^2} K[1] K[2] F'\left (e^{-\frac {1}{4} K[1]^2} K[2]\right )}{2 F\left (e^{-\frac {1}{4} K[1]^2} K[2]\right )^2}\right ) \, dK[1]+1\right )}{F\left (e^{-\frac {x^2}{4}} K[2]\right )} \, dK[2]+\int _1^x \left (\frac {y(x) e^{-\frac {1}{4} K[1]^2} K[1]}{2 F\left (y(x) e^{-\frac {1}{4} K[1]^2}\right )}+1\right ) \, dK[1]=c_1,y(x)\right ] \]
Maple: cpu = 0.110 (sec), leaf count = 27 \[ \left \{ y \left ( x \right ) ={{\it RootOf} \left ( -x+\int ^{{\it \_Z}} \! \left ( F \left ( {\it \_a} \right ) \right ) ^{-1}{d{\it \_a}}+{\it \_C1} \right ) \left ( {{\rm e}^{-{\frac {{x}^{2}}{4}}}} \right ) ^{-1}} \right \} \]