\[ y'(x)=\frac {e^{-\frac {3 x^2}{2}} x y(x)^3}{3 \left (e^{\frac {3 x^2}{2}} y(x)+3 e^{\frac {3 x^2}{2}}+3 y(x)\right )} \] ✓ Mathematica : cpu = 9.2938 (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 = 1.363 (sec), leaf count = 143
\[y \relax (x ) = \RootOf \left (\left (7 \,{\mathrm e}^{3 x^{2}+\RootOf \left ({\mathrm e}^{3 x^{2}} \left (217 \left (\tanh ^{2}\left (\frac {\left (c_{1}-5 \textit {\_Z} \right ) \sqrt {93}}{90}\right )\right ) {\mathrm e}^{3 x^{2}+\textit {\_Z}}+42 \tanh \left (\frac {\left (c_{1}-5 \textit {\_Z} \right ) \sqrt {93}}{90}\right ) \sqrt {93}\, {\mathrm e}^{3 x^{2}+\textit {\_Z}}+189 \,{\mathrm e}^{3 x^{2}+\textit {\_Z}}-93 \left (\tanh ^{2}\left (\frac {\left (c_{1}-5 \textit {\_Z} \right ) \sqrt {93}}{90}\right )\right )+93\right )\right )}+9 \,{\mathrm e}^{3 x^{2}}+27 \,{\mathrm e}^{\frac {3 x^{2}}{2}}-3\right ) \textit {\_Z}^{2}+81+\left (54 \,{\mathrm e}^{\frac {3 x^{2}}{2}}+81\right ) \textit {\_Z} \right ) {\mathrm e}^{\frac {3 x^{2}}{2}}\]