\[ y'(x)=\frac {e^{-2 b x} y(x)^3}{e^{-b x} y(x)+1} \] ✓ Mathematica : cpu = 1.00245 (sec), leaf count = 90
DSolve[Derivative[1][y][x] == y[x]^3/(E^(2*b*x)*(1 + y[x]/E^(b*x))),y[x],x]
\[\text {Solve}\left [\frac {\log (y(x))}{b}+\frac {1}{2} \left (-\frac {\log \left (y(x)^2-b e^{b x} \left (e^{b x}+y(x)\right )\right )}{b}+\frac {2 \tanh ^{-1}\left (\frac {\sqrt {\frac {b}{b+4}} \left (2 e^{b x}+y(x)\right )}{y(x)}\right )}{\sqrt {b} \sqrt {b+4}}+2 x\right )=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.283 (sec), leaf count = 82
dsolve(diff(y(x),x) = y(x)^3/(y(x)*exp(-b*x)+1)*exp(-2*b*x),y(x))
\[b x -\frac {b \arctanh \left (\frac {-2 y \left (x \right ) {\mathrm e}^{-b x}+b}{\sqrt {b^{2}+4 b}}\right )}{\sqrt {b^{2}+4 b}}-\frac {\ln \left (-b y \left (x \right ) {\mathrm e}^{-b x}+y \left (x \right )^{2} {\mathrm e}^{-2 b x}-b \right )}{2}+\ln \left (y \left (x \right ) {\mathrm e}^{-b x}\right )-c_{1} = 0\]