2.796 ODE No. 796
\[ y'(x)=\frac {e^{-\frac {3 x^2}{2}} x y(x)^3}{3 \left (e^{\frac {3 x^2}{2}} y(x)+3 e^{\frac {3 x^2}{2}}+3 y(x)\right )} \]
✓ Mathematica : cpu = 7.62071 (sec), leaf count = 109
DSolve[Derivative[1][y][x] == (x*y[x]^3)/(3*E^((3*x^2)/2)*(3*E^((3*x^2)/2) + 3*y[x] + E^((3*x^2)/2)*y[x])),y[x],x]
\[\text {Solve}\left [\frac {1}{62} \left (-31 \log \left (9 e^{\frac {3 x^2}{2}} (y(x)+3) y(x)+3 e^{3 x^2} (y(x)+3)^2-y(x)^2\right )+6 \sqrt {93} \tanh ^{-1}\left (\frac {\sqrt {\frac {3}{31}} \left (2 e^{\frac {3 x^2}{2}} (y(x)+3)+3 y(x)\right )}{y(x)}\right )+62 \log \left (e^{\frac {3 x^2}{2}}\right )\right )+\log (y(x))=c_1,y(x)\right ]\]
✓ Maple : cpu = 1.664 (sec), leaf count = 143
dsolve(diff(y(x),x) = 1/3*y(x)^3*x*exp(3*x^2)/(3*exp(3/2*x^2)+exp(3/2*x^2)*y(x)+3*y(x))/exp(9/2*x^2),y(x))
\[y \left (x \right ) = \operatorname {RootOf}\left (\left (7 \,{\mathrm e}^{3 x^{2}+\operatorname {RootOf}\left ({\mathrm e}^{3 x^{2}} \left (42 \sqrt {93}\, \tanh \left (\frac {\left (c_{1} -5 \textit {\_Z} \right ) \sqrt {93}}{90}\right ) {\mathrm e}^{3 x^{2}+\textit {\_Z}}+217 \tanh \left (\frac {\left (c_{1} -5 \textit {\_Z} \right ) \sqrt {93}}{90}\right )^{2} {\mathrm e}^{3 x^{2}+\textit {\_Z}}+189 \,{\mathrm e}^{3 x^{2}+\textit {\_Z}}-93 \tanh \left (\frac {\left (c_{1} -5 \textit {\_Z} \right ) \sqrt {93}}{90}\right )^{2}+93\right )\right )}+9 \,{\mathrm e}^{3 x^{2}}+27 \,{\mathrm e}^{\frac {3 x^{2}}{2}}-3\right ) \textit {\_Z}^{2}+81+\left (54 \,{\mathrm e}^{\frac {3 x^{2}}{2}}+81\right ) \textit {\_Z} \right ) {\mathrm e}^{\frac {3 x^{2}}{2}}\]