\[ y'(x)=\frac {e^{2 x^2} x y(x)^3}{e^{x^2} y(x)+1} \] ✓ Mathematica : cpu = 8.62443 (sec), leaf count = 68
DSolve[Derivative[1][y][x] == (E^(2*x^2)*x*y[x]^3)/(1 + E^x^2*y[x]),y[x],x]
\[\text {Solve}\left [\log (y(x))-2 y(x)^2 \left (\frac {\log \left (e^{2 x^2} y(x)^2+2 e^{x^2} y(x)+2\right )}{4 y(x)^2}-\frac {\tan ^{-1}\left (e^{x^2} y(x)+1\right )}{2 y(x)^2}\right )=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.206 (sec), leaf count = 85
dsolve(diff(y(x),x) = y(x)^3/(y(x)*exp(x^2)+1)*x*exp(2*x^2),y(x))
\[y \left (x \right ) = \frac {\left (-\tan \left (\RootOf \left (-2 x^{2}-\ln \left (\frac {81 \left (\tan ^{2}\left (\textit {\_Z} \right )\right )}{10}+\frac {81}{10}\right )+2 \ln \left (\frac {9 \tan \left (\textit {\_Z} \right )}{2}-\frac {9}{2}\right )+6 c_{1}-2 \textit {\_Z} \right )\right )+1\right ) {\mathrm e}^{-x^{2}}}{\tan \left (\RootOf \left (-2 x^{2}-\ln \left (\frac {81 \left (\tan ^{2}\left (\textit {\_Z} \right )\right )}{10}+\frac {81}{10}\right )+2 \ln \left (\frac {9 \tan \left (\textit {\_Z} \right )}{2}-\frac {9}{2}\right )+6 c_{1}-2 \textit {\_Z} \right )\right )}\]