\[ y'(x)=\frac {e^{3 x^2} x (y(x)+3)^3}{81 \left (e^{\frac {3 x^2}{2}} y(x)+3 e^{\frac {3 x^2}{2}}+3 y(x)\right )} \] ✓ Mathematica : cpu = 7.81026 (sec), leaf count = 103
DSolve[Derivative[1][y][x] == (E^(3*x^2)*x*(3 + y[x])^3)/(81*(3*E^((3*x^2)/2) + 3*y[x] + E^((3*x^2)/2)*y[x])),y[x],x]
\[\text {Solve}\left [\frac {1}{186} \left (6 \sqrt {93} \text {arctanh}\left (\frac {81 y(x)-2 e^{\frac {3 x^2}{2}} (y(x)+3)}{9 \sqrt {93} y(x)}\right )+31 \log \left (-81 e^{\frac {3 x^2}{2}} (y(x)+3) y(x)+e^{3 x^2} (y(x)+3)^2-243 y(x)^2\right )\right )-\frac {1}{3} \log (y(x)+3)=c_1,y(x)\right ]\] ✓ Maple : cpu = 1.47 (sec), leaf count = 168
dsolve(diff(y(x),x) = 1/81*(3+y(x))^3*exp(9/2*x^2)*x*exp(3/2*x^2)/(3*exp(3/2*x^2)+exp(3/2*x^2)*y(x)+3*y(x))/exp(3*x^2),y(x))
\[5 \ln \left (\frac {\frac {100 \left (3+y \left (x \right )\right )^{2} {\mathrm e}^{3 x^{2}}}{189}+\frac {300 \left (-y \left (x \right )^{2}-3 y \left (x \right )\right ) {\mathrm e}^{\frac {3 x^{2}}{2}}}{7}-\frac {900 y \left (x \right )^{2}}{7}}{\left ({\mathrm e}^{\frac {3 x^{2}}{2}} \left (3+y \left (x \right )\right )+3 y \left (x \right )\right )^{2}}\right )-\frac {30 \sqrt {93}\, \operatorname {arctanh}\left (\frac {\left (29 \,{\mathrm e}^{\frac {3 x^{2}}{2}} y \left (x \right )+87 \,{\mathrm e}^{\frac {3 x^{2}}{2}}+81 y \left (x \right )\right ) \sqrt {93}}{\left (279 y \left (x \right )+837\right ) {\mathrm e}^{\frac {3 x^{2}}{2}}+837 y \left (x \right )}\right )}{31}-10 \ln \left (\frac {10 \,{\mathrm e}^{\frac {3 x^{2}}{2}} \left (3+y \left (x \right )\right )}{9 \left (3 \,{\mathrm e}^{\frac {3 x^{2}}{2}}+{\mathrm e}^{\frac {3 x^{2}}{2}} y \left (x \right )+3 y \left (x \right )\right )}\right )+15 x^{2}-c_{1} = 0\]