\[ y'(x)=\frac {e^{3 x^2} x (y(x)+3)^3}{81 \left (e^{\frac {3 x^2}{2}} y(x)+3 e^{\frac {3 x^2}{2}}+3 y(x)\right )} \] ✓ Mathematica : cpu = 19.1853 (sec), leaf count = 103
\[\text {Solve}\left [\frac {1}{186} \left (31 \log \left (-81 e^{\frac {3 x^2}{2}} (y(x)+3) y(x)+e^{3 x^2} (y(x)+3)^2-243 y(x)^2\right )-6 \sqrt {93} \tanh ^{-1}\left (\frac {2 e^{\frac {3 x^2}{2}} (y(x)+3)-81 y(x)}{9 \sqrt {93} y(x)}\right )\right )-\frac {1}{3} \log (y(x)+3)=c_1,y(x)\right ]\] ✓ Maple : cpu = 1.004 (sec), leaf count = 168
\[ \left \{ -10\,\ln \left ( {\frac {10\,{{\rm e}^{3/2\,{x}^{2}}} \left ( 3+y \left ( x \right ) \right ) }{27\,{{\rm e}^{3/2\,{x}^{2}}}+9\,{{\rm e}^{3/2\,{x}^{2}}}y \left ( x \right ) +27\,y \left ( x \right ) }} \right ) +5\,\ln \left ( {\frac {100\, \left ( 3+y \left ( x \right ) \right ) ^{2} \left ( {{\rm e}^{3/2\,{x}^{2}}} \right ) ^{2}+ \left ( -8100\, \left ( y \left ( x \right ) \right ) ^{2}-24300\,y \left ( x \right ) \right ) {{\rm e}^{3/2\,{x}^{2}}}-24300\, \left ( y \left ( x \right ) \right ) ^{2}}{189\, \left ( {{\rm e}^{3/2\,{x}^{2}}} \left ( 3+y \left ( x \right ) \right ) +3\,y \left ( x \right ) \right ) ^{2}}} \right ) -{\frac {30\,\sqrt {93}}{31}{\it Artanh} \left ( {\sqrt {93} \left ( 29\,{{\rm e}^{3/2\,{x}^{2}}}y \left ( x \right ) +87\,{{\rm e}^{3/2\,{x}^{2}}}+81\,y \left ( x \right ) \right ) \left ( \left ( 279\,y \left ( x \right ) +837 \right ) {{\rm e}^{{\frac {3\,{x}^{2}}{2}}}}+837\,y \left ( x \right ) \right ) ^{-1}} \right ) }+15\,{x}^{2}-{\it \_C1}=0 \right \} \]