\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) = \left ( 1+ \left ( y \left ( x \right ) \right ) ^{2}{{\rm e}^{2\,{x}^{2}}}+ \left ( y \left ( x \right ) \right ) ^{3}{{\rm e}^{3\,{x}^{2}}} \right ) {{\rm e}^{-{x}^{2}}}x=0} \]
Mathematica: cpu = 0.129517 (sec), leaf count = 127 \[ \text {Solve}\left [\frac {11}{3} \text {RootSum}\left [11 \text {$\#$1}^3+15 \sqrt [3]{11} \text {$\#$1}+11\& ,\frac {\log \left (\frac {3 e^{2 x^2} x y(x)+e^{x^2} x}{\sqrt [3]{11} \sqrt [3]{e^{3 x^2} x^3}}-\text {$\#$1}\right )}{11 \text {$\#$1}^2+5 \sqrt [3]{11}}\& \right ]=c_1+\frac {11^{2/3} e^{x^2} x^3}{18 \sqrt [3]{e^{3 x^2} x^3}},y(x)\right ] \]
Maple: cpu = 0.063 (sec), leaf count = 44 \[ \left \{ y \left ( x \right ) =-{\frac {11\,{\it RootOf} \left ( -5\,{x}^ {2}+20250\,\int ^{{\it \_Z}}\! \left ( 121\,{{\it \_a}}^{3}+3375\,{\it \_a}-3375 \right ) ^{-1}{d{\it \_a}}+6\,{\it \_C1} \right ) +15}{45\,{ {\rm e}^{{x}^{2}}}}} \right \} \]