\[ y'(x)=e^{-x^2} x \left (e^{3 x^2} y(x)^3+e^{2 x^2} y(x)^2+1\right ) \] ✓ Mathematica : cpu = 0.33927 (sec), leaf count = 127
DSolve[Derivative[1][y][x] == (x*(1 + E^(2*x^2)*y[x]^2 + E^(3*x^2)*y[x]^3))/E^x^2,y[x],x]
\[\text {Solve}\left [\frac {11}{3} \text {RootSum}\left [11 \text {$\#$1}^3+15 \sqrt [3]{11} \text {$\#$1}+11\& ,\frac {\log \left (\frac {3 e^{2 x^2} x y(x)+e^{x^2} x}{\sqrt [3]{11} \sqrt [3]{e^{3 x^2} x^3}}-\text {$\#$1}\right )}{11 \text {$\#$1}^2+5 \sqrt [3]{11}}\& \right ]=\frac {11^{2/3} e^{x^2} x^3}{18 \sqrt [3]{e^{3 x^2} x^3}}+c_1,y(x)\right ]\] ✓ Maple : cpu = 0.08 (sec), leaf count = 44
dsolve(diff(y(x),x) = (1+y(x)^2*exp(2*x^2)+y(x)^3*exp(3*x^2))*exp(-x^2)*x,y(x))
\[y \left (x \right ) = \frac {\left (-11 \RootOf \left (-5 x^{2}+20250 \left (\int _{}^{\textit {\_Z}}\frac {1}{121 \textit {\_a}^{3}+3375 \textit {\_a} -3375}d \textit {\_a} \right )+6 c_{1}\right )-15\right ) {\mathrm e}^{-x^{2}}}{45}\]