\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) =-1/8\, \left ( -8\,{{\rm e}^{-{x}^{2}}}+8\,{x}^{2}{{\rm e}^{-{x}^{2}}}-8-8\, \left ( y \left ( x \right ) \right ) ^{2}+8\,{x}^{2}{{\rm e}^{-{x}^{2}}}y \left ( x \right ) -2\,{x}^{4} \left ( {{\rm e}^{-{x}^{2}}} \right ) ^{2}-8\, \left ( y \left ( x \right ) \right ) ^{3}+12\,{x}^{2}{{\rm e}^{-{x}^{2}}} \left ( y \left ( x \right ) \right ) ^{2}-6\,y \left ( x \right ) {x}^{4} \left ( {{\rm e}^{-{x}^{2}}} \right ) ^{2}+{x}^{6} \left ( {{\rm e}^{-{x}^{2}}} \right ) ^{3} \right ) x=0} \]
Mathematica: cpu = 0.139518 (sec), leaf count = 112 \[ \text {Solve}\left [-\frac {29}{3} \text {RootSum}\left [-29 \text {$\#$1}^3+3 \sqrt [3]{29} \text {$\#$1}-29\& ,\frac {\log \left (\frac {\frac {1}{2} e^{-x^2} x \left (2 e^{x^2}-3 x^2\right )+3 x y(x)}{\sqrt [3]{29} \sqrt [3]{x^3}}-\text {$\#$1}\right )}{\sqrt [3]{29}-29 \text {$\#$1}^2}\& \right ]=c_1+\frac {1}{18} 29^{2/3} \left (x^3\right )^{2/3},y(x)\right ] \]
Maple: cpu = 0.078 (sec), leaf count = 72 \[ \left \{ y \left ( x \right ) =-{\frac {-9\,{x}^{2}{{\rm e}^{-{x}^{2}}}+ 6\,{{\rm e}^{-{x}^{2}}}{{\rm e}^{{x}^{2}}}-58\,{\it RootOf} \left ( {x} ^{2}-162\,\int ^{{\it \_Z}}\! \left ( 841\,{{\it \_a}}^{3}-27\,{\it \_a }+27 \right ) ^{-1}{d{\it \_a}}+6\,{\it \_C1} \right ) }{18\,{{\rm e}^{- {x}^{2}}}{{\rm e}^{{x}^{2}}}}} \right \} \]