\[ y'(x)=-\frac {1}{8} x \left (12 e^{-x^2} x^2 y(x)^2+8 e^{-x^2} x^2 y(x)+8 e^{-x^2} x^2-8 e^{-x^2}+e^{-3 x^2} x^6-6 e^{-2 x^2} x^4 y(x)-2 e^{-2 x^2} x^4-8 y(x)^3-8 y(x)^2-8\right ) \] ✓ Mathematica : cpu = 0.153623 (sec), leaf count = 100
\[\text {Solve}\left [174 \text {RootSum}\left [-29 \text {$\#$1}^3+3 \sqrt [3]{29} \text {$\#$1}-29\& ,\frac {\log \left (\frac {-\frac {3}{2} e^{-x^2} x^3+3 x y(x)+x}{\sqrt [3]{29} \sqrt [3]{x^3}}-\text {$\#$1}\right )}{\sqrt [3]{29}-29 \text {$\#$1}^2}\& \right ]+18 c_1+29^{2/3} \left (x^3\right )^{2/3}=0,y(x)\right ]\]
✓ Maple : cpu = 0.134 (sec), leaf count = 68
\[ \left \{ y \left ( x \right ) ={\frac {58\,{\it RootOf} \left ( {x}^{2}-162\,\int ^{{\it \_Z}}\! \left ( 841\,{{\it \_a}}^{3}-27\,{\it \_a}+27 \right ) ^{-1}{d{\it \_a}}+6\,{\it \_C1} \right ) + \left ( 9\,{x}^{2}-6\,{{\rm e}^{{x}^{2}}} \right ) {{\rm e}^{-{x}^{2}}}}{18\,{{\rm e}^{-{x}^{2}}}{{\rm e}^{{x}^{2}}}}} \right \} \]