\[ y'(x)=\frac {e^{-\frac {3 x^2}{2}} x y(x)^3}{3 \left (e^{\frac {3 x^2}{2}} y(x)+3 e^{\frac {3 x^2}{2}}+3 y(x)\right )} \] ✓ Mathematica : cpu = 12.1357 (sec), leaf count = 102
\[\text {Solve}\left [\frac {1}{62} \left (-31 \log \left (9 e^{\frac {3 x^2}{2}} (y(x)+3) y(x)+3 e^{3 x^2} (y(x)+3)^2-y(x)^2\right )+6 \sqrt {93} \tanh ^{-1}\left (\frac {\sqrt {\frac {3}{31}} \left (2 e^{\frac {3 x^2}{2}} (y(x)+3)+3 y(x)\right )}{y(x)}\right )+93 x^2\right )+\log (y(x))=c_1,y(x)\right ]\] ✓ Maple : cpu = 3.665 (sec), leaf count = 143
\[ \left \{ y \left ( x \right ) ={\it RootOf} \left ( \left ( 7\,{{\rm e}^{3\,{x}^{2}+{\it RootOf} \left ( \left ( {{\rm e}^{3/2\,{x}^{2}}} \right ) ^{2} \left ( 42\,\sqrt {93}\tanh \left ( {\frac { \left ( {\it \_C1}-5\,{\it \_Z} \right ) \sqrt {93}}{90}} \right ) {{\rm e}^{3\,{x}^{2}+{\it \_Z}}}+217\, \left ( \tanh \left ( {\frac { \left ( {\it \_C1}-5\,{\it \_Z} \right ) \sqrt {93}}{90}} \right ) \right ) ^{2}{{\rm e}^{3\,{x}^{2}+{\it \_Z}}}+189\,{{\rm e}^{3\,{x}^{2}+{\it \_Z}}}-93\, \left ( \tanh \left ( {\frac { \left ( {\it \_C1}-5\,{\it \_Z} \right ) \sqrt {93}}{90}} \right ) \right ) ^{2}+93 \right ) \right ) }}+9\, \left ( {{\rm e}^{3/2\,{x}^{2}}} \right ) ^{2}+27\,{{\rm e}^{3/2\,{x}^{2}}}-3 \right ) {{\it \_Z}}^{2}+81+ \left ( 54\,{{\rm e}^{3/2\,{x}^{2}}}+81 \right ) {\it \_Z} \right ) {{\rm e}^{{\frac {3\,{x}^{2}}{2}}}} \right \} \]