\[ y'(x)=e^{2 x^2} x y(x) \left (e^{-x^2} y(x)+e^{-2 x^2}+y(x)^2\right ) \] ✓ Mathematica : cpu = 0.386356 (sec), leaf count = 139
DSolve[Derivative[1][y][x] == E^(2*x^2)*x*y[x]*(E^(-2*x^2) + y[x]/E^x^2 + y[x]^2),y[x],x]
\[\text {Solve}\left [-\frac {25}{3} \text {RootSum}\left [-25 \text {$\#$1}^3+24 \sqrt [3]{-1} 5^{2/3} \text {$\#$1}-25\& ,\frac {\log \left (\frac {3 e^{2 x^2} x y(x)+e^{x^2} x}{5^{2/3} \sqrt [3]{-e^{3 x^2} x^3}}-\text {$\#$1}\right )}{8 \sqrt [3]{-1} 5^{2/3}-25 \text {$\#$1}^2}\& \right ]=-\frac {5 \sqrt [3]{5} e^{x^2} x^3}{18 \sqrt [3]{-e^{3 x^2} x^3}}+c_1,y(x)\right ]\] ✓ Maple : cpu = 0.195 (sec), leaf count = 122
dsolve(diff(y(x),x) = y(x)*(y(x)^2+exp(-x^2)*y(x)+exp(-x^2)^2)/exp(-x^2)^2*x,y(x))
\[y \left (x \right ) = \frac {\left (\sqrt {11}\, \tan \left (\RootOf \left (-4 \sqrt {11}\, x^{2}+4 \sqrt {11}\, \ln \left (11\right )+8 \sqrt {11}\, \ln \left (-\frac {36 \sqrt {11}}{11}+36 \tan \left (\textit {\_Z} \right )\right )-4 \sqrt {11}\, \ln \left (\frac {14256 \,{\mathrm e}^{2 x^{2}} \left (\tan ^{2}\left (\textit {\_Z} \right )\right )}{25}+\frac {14256 \,{\mathrm e}^{2 x^{2}}}{25}\right )+9 \sqrt {11}\, c_{1}-8 \textit {\_Z} \right )\right )-1\right ) {\mathrm e}^{-x^{2}}}{2}\]