\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac {x{{\rm e}^{-{x}^{2}}}}{y \left ( x \right ) {{\rm e}^{{x}^{2}}}+1}}=0} \]
Mathematica: cpu = 9.663227 (sec), leaf count = 59 \[ \text {Solve}\left [-\frac {1}{4} \log \left (2 e^{2 x^2} y(x)^2+2 e^{x^2} y(x)+1\right )-\frac {1}{2} \tan ^{-1}\left (2 e^{x^2} y(x)+1\right )+\frac {x^2}{2}=c_1,y(x)\right ] \]
Maple: cpu = 1.482 (sec), leaf count = 84 \[ \left \{ y \left ( x \right ) =-{\frac {1}{{{\rm e}^{{x}^{2}}}}\tan \left ( {\it RootOf} \left ( 2\,{x}^{2}-\ln \left ( {\frac {81\, \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}}{10}}+{\frac {81}{ 10}} \right ) +2\,\ln \left ( 9/2\,\tan \left ( {\it \_Z} \right ) -9/2 \right ) +6\,{\it \_C1}-2\,{\it \_Z} \right ) \right ) \left ( \tan \left ( {\it RootOf} \left ( 2\,{x}^{2}-\ln \left ( {\frac {81\, \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}}{10}}+{\frac {81}{ 10}} \right ) +2\,\ln \left ( 9/2\,\tan \left ( {\it \_Z} \right ) -9/2 \right ) +6\,{\it \_C1}-2\,{\it \_Z} \right ) \right ) -1 \right ) ^{-1} } \right \} \]