\[ y'(x)=\frac {e^{3 x^2} x (y(x)+3)^3}{81 \left (e^{\frac {3 x^2}{2}} y(x)+3 e^{\frac {3 x^2}{2}}+3 y(x)\right )} \] ✓ Mathematica : cpu = 18.1846 (sec), leaf count = 100
\[\text {Solve}\left [\frac {1}{6} \left (\log \left (-81 e^{\frac {3 x^2}{2}} (y(x)+3) y(x)+e^{3 x^2} (y(x)+3)^2-243 y(x)^2\right )-2 \log (y(x)+3)\right )=c_1+\sqrt {\frac {3}{31}} \tanh ^{-1}\left (\frac {2 e^{\frac {3 x^2}{2}} (y(x)+3)-81 y(x)}{9 \sqrt {93} y(x)}\right ),y(x)\right ]\]
✓ Maple : cpu = 0.829 (sec), leaf count = 168
\[ \left \{ 5\,\ln \left ( {\frac {100\, \left ( 3+y \left ( x \right ) \right ) ^{2} \left ( {{\rm e}^{3/2\,{x}^{2}}} \right ) ^{2}+ \left ( -8100\, \left ( y \left ( x \right ) \right ) ^{2}-24300\,y \left ( x \right ) \right ) {{\rm e}^{3/2\,{x}^{2}}}-24300\, \left ( y \left ( x \right ) \right ) ^{2}}{189\, \left ( {{\rm e}^{3/2\,{x}^{2}}} \left ( 3+y \left ( x \right ) \right ) +3\,y \left ( x \right ) \right ) ^{2}}} \right ) -{\frac {30\,\sqrt {93}}{31}{\it Artanh} \left ( {\sqrt {93} \left ( 29\,{{\rm e}^{3/2\,{x}^{2}}}y \left ( x \right ) +87\,{{\rm e}^{3/2\,{x}^{2}}}+81\,y \left ( x \right ) \right ) \left ( \left ( 279\,y \left ( x \right ) +837 \right ) {{\rm e}^{{\frac {3\,{x}^{2}}{2}}}}+837\,y \left ( x \right ) \right ) ^{-1}} \right ) }-10\,\ln \left ( {\frac {10\,{{\rm e}^{3/2\,{x}^{2}}} \left ( 3+y \left ( x \right ) \right ) }{27\,{{\rm e}^{3/2\,{x}^{2}}}+9\,{{\rm e}^{3/2\,{x}^{2}}}y \left ( x \right ) +27\,y \left ( x \right ) }} \right ) +15\,{x}^{2}-{\it \_C1}=0 \right \} \]