\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac {x \left ( y \left ( x \right ) \right ) ^{3}{{\rm e}^{2\,{x}^{2}}}}{y \left ( x \right ) {{\rm e}^{{x}^{2}}}+1}}=0} \]
Mathematica: cpu = 9.256675 (sec), leaf count = 68 \[ \text {Solve}\left [\log (y(x))-2 y(x)^2 \left (\frac {\log \left (e^{2 x^2} y(x)^2+2 e^{x^2} y(x)+2\right )}{4 y(x)^2}-\frac {\tan ^{-1}\left (e^{x^2} y(x)+1\right )}{2 y(x)^2}\right )=c_1,y(x)\right ] \]
Maple: cpu = 1.482 (sec), leaf count = 85 \[ \left \{ y \left ( x \right ) ={\frac {1}{{{\rm e}^{{x}^{2}}}} \left ( - \tan \left ( {\it RootOf} \left ( -2\,{x}^{2}-\ln \left ( {\frac {81\, \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}}{10}}+{\frac {81}{ 10}} \right ) +2\,\ln \left ( 9/2\,\tan \left ( {\it \_Z} \right ) -9/2 \right ) +6\,{\it \_C1}-2\,{\it \_Z} \right ) \right ) +1 \right ) \left ( \tan \left ( {\it RootOf} \left ( -2\,{x}^{2}-\ln \left ( { \frac {81\, \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}}{10}}+{ \frac {81}{10}} \right ) +2\,\ln \left ( 9/2\,\tan \left ( {\it \_Z} \right ) -9/2 \right ) +6\,{\it \_C1}-2\,{\it \_Z} \right ) \right ) \right ) ^{-1}} \right \} \]