\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) =1/4\, \left ( 4\,{{\rm e}^{-{x}^{2}}}-4\,{x}^{2}{{\rm e}^{-{x}^{2}}}+4\, \left ( y \left ( x \right ) \right ) ^{2}-4\,{x}^{2}{{\rm e}^{-{x}^{2}}}y \left ( x \right ) +{x}^{4} \left ( {{\rm e}^{-{x}^{2}}} \right ) ^{2} \right ) x=0} \]
Mathematica: cpu = 0.042005 (sec), leaf count = 32 \[ \left \{\left \{y(x)\to \frac {1}{c_1-\frac {x^2}{2}}+\frac {1}{2} e^{-x^2} x^2\right \}\right \} \]
Maple: cpu = 0.109 (sec), leaf count = 25 \[ \left \{ y \left ( x \right ) ={\frac {{x}^{2}{{\rm e}^{-{x}^{2}}}}{2}}+ \left ( {\it \_C1}-{\frac {{x}^{2}}{2}} \right ) ^{-1} \right \} \]