\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac { \left ( y \left ( x \right ) \right ) ^{3}{{\rm e}^{-2\,bx}}}{y \left ( x \right ) {{\rm e}^{-bx}}+1}}=0} \]
Mathematica: cpu = 1.021630 (sec), leaf count = 90 \[ \text {Solve}\left [\frac {\log (y(x))}{b}+\frac {1}{2} \left (-\frac {\log \left (y(x)^2-b e^{b x} \left (e^{b x}+y(x)\right )\right )}{b}+\frac {2 \tanh ^{-1}\left (\frac {\sqrt {\frac {b}{b+4}} \left (2 e^{b x}+y(x)\right )}{y(x)}\right )}{\sqrt {b} \sqrt {b+4}}+2 x\right )=c_1,y(x)\right ] \]
Maple: cpu = 0.172 (sec), leaf count = 83 \[ \left \{ bx+{b{\it Artanh} \left ( {(2\,y \left ( x \right ) {{\rm e}^{-b x}}-b){\frac {1}{\sqrt {{b}^{2}+4\,b}}}} \right ) {\frac {1}{\sqrt {{b} ^{2}+4\,b}}}}+\ln \left ( y \left ( x \right ) {{\rm e}^{-bx}} \right ) - {\frac {\ln \left ( -by \left ( x \right ) {{\rm e}^{-bx}}+ \left ( y \left ( x \right ) \right ) ^{2} \left ( {{\rm e}^{-bx}} \right ) ^{2}-b \right ) }{2}}-{\it \_C1}=0 \right \} \]