#### 2.667   ODE No. 667

$y'(x)=\frac {e^{-2 b x} y(x)^3}{e^{-b x} y(x)+1}$ Mathematica : cpu = 0.926587 (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 = 0.163 (sec), leaf count = 82

$\left \{ bx-{b{\it Artanh} \left ( {(-2\,y \left ( x \right ) {{\rm e}^{-bx}}+b){\frac {1}{\sqrt {{b}^{2}+4\,b}}}} \right ) {\frac {1}{\sqrt {{b}^{2}+4\,b}}}}+\ln \left ( y \left ( x \right ) {{\rm e}^{-bx}} \right ) -{\frac {\ln \left ( -by \left ( x \right ) {{\rm e}^{-bx}}+ \left ( y \left ( x \right ) \right ) ^{2} \left ( {{\rm e}^{-bx}} \right ) ^{2}-b \right ) }{2}}-{\it \_C1}=0 \right \}$
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