\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac { \left ( 3+y \left ( x \right ) \right ) ^{3}{{\rm e}^{9/2\,{x}^{2}}}x{{\rm e}^{3/2\,{x}^{2}}}}{ \left ( 243\,{{\rm e}^{3/2\,{x}^{2}}}+81\,{{\rm e}^{3/2\,{x}^{2}}}y \left ( x \right ) +243\,y \left ( x \right ) \right ) {{\rm e}^{3\,{x}^{2}}}}}=0} \]
Mathematica: cpu = 10.172792 (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 = 1.326 (sec), leaf count = 202 \[ \left \{ 5\,\ln \left ( {\frac {100\, \left ( {{\rm e}^{3/2\,{x}^{2}}} \right ) ^{2} \left ( y \left ( x \right ) \right ) ^{2}+600\, \left ( { {\rm e}^{3/2\,{x}^{2}}} \right ) ^{2}y \left ( x \right ) -8100\, \left ( y \left ( x \right ) \right ) ^{2}{{\rm e}^{3/2\,{x}^{2}}}+900\, \left ( {{\rm e}^{3/2\,{x}^{2}}} \right ) ^{2}-24300\,{{\rm e}^{3/2\,{x}^{2}}}y \left ( x \right ) -24300\, \left ( y \left ( x \right ) \right ) ^{2}}{ 189\, \left ( 3\,{{\rm e}^{3/2\,{x}^{2}}}+{{\rm e}^{3/2\,{x}^{2}}}y \left ( x \right ) +3\,y \left ( x \right ) \right ) ^{2}}} \right ) -{ \frac {30\,\sqrt {93}}{31}{\it Artanh} \left ( {\frac {\sqrt {93}}{279} \left ( 29\,{{\rm e}^{3/2\,{x}^{2}}}y \left ( x \right ) +87\,{{\rm e}^{ 3/2\,{x}^{2}}}+81\,y \left ( x \right ) \right ) \left ( 3\,{{\rm e}^{3/ 2\,{x}^{2}}}+{{\rm e}^{{\frac {3\,{x}^{2}}{2}}}}y \left ( x \right ) +3 \,y \left ( x \right ) \right ) ^{-1}} \right ) }-10\,\ln \left ( {\frac {10\,{{\rm e}^{3/2\,{x}^{2}}} \left ( 3+y \left ( x \right ) \right ) }{ 27\,{{\rm e}^{3/2\,{x}^{2}}}+9\,{{\rm e}^{3/2\,{x}^{2}}}y \left ( x \right ) +27\,y \left ( x \right ) }} \right ) +15\,{x}^{2}-{\it \_C1}=0 \right \} \]