\[ y'(x)=\frac {e^{-2 x} y(x)^3}{e^{-x} y(x)+1} \] ✓ Mathematica : cpu = 0.510395 (sec), leaf count = 73
DSolve[Derivative[1][y][x] == y[x]^3/(E^(2*x)*(1 + y[x]/E^x)),y[x],x]
\[\text {Solve}\left [\log (y(x))+\frac {1}{10} \left (-\left (5+\sqrt {5}\right ) \log \left (-\sqrt {5} y(x)+y(x)+2 e^x\right )+\left (\sqrt {5}-5\right ) \log \left (\sqrt {5} y(x)+y(x)+2 e^x\right )+10 \log \left (e^x\right )\right )=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.977 (sec), leaf count = 58
dsolve(diff(y(x),x) = 1/(y(x)*exp(-x)+1)*y(x)^3*exp(-2*x),y(x))
\[y \left (x \right ) = {\mathrm e}^{\operatorname {RootOf}\left (2 \sqrt {5}\, \operatorname {arctanh}\left (\frac {\left (-2 \,{\mathrm e}^{\textit {\_Z}}+{\mathrm e}^{x}\right ) \sqrt {5}\, {\mathrm e}^{-x}}{5}\right )+5 \ln \left ({\mathrm e}^{2 \textit {\_Z}}-{\mathrm e}^{x +\textit {\_Z}}-{\mathrm e}^{2 x}\right )+10 c_{1}-10 \textit {\_Z} -10 x \right )}\]