#### 2.668   ODE No. 668

$y'(x)=\frac {e^{-2 x} y(x)^3}{e^{-x} y(x)+1}$ Mathematica : cpu = 0.595035 (sec), leaf count = 78

$\text {Solve}\left [\log (y(x))+y(x)^2 \left (\frac {x}{y(x)^2}-\frac {\log \left (-y(x)^2+e^x y(x)+e^{2 x}\right )}{2 y(x)^2}+\frac {\tanh ^{-1}\left (\frac {y(x)+2 e^x}{\sqrt {5} y(x)}\right )}{\sqrt {5} y(x)^2}\right )=c_1,y(x)\right ]$ Maple : cpu = 0.549 (sec), leaf count = 58

$\left \{ y \left ( x \right ) ={{\rm e}^{{\it RootOf} \left ( 2\,\sqrt {5}{\it Artanh} \left ( 1/5\,{\frac { \left ( -2\,{{\rm e}^{{\it \_Z}}}+{{\rm e}^{x}} \right ) \sqrt {5}}{{{\rm e}^{x}}}} \right ) +5\,\ln \left ( - \left ( {{\rm e}^{x}} \right ) ^{2}-{{\rm e}^{{\it \_Z}+x}}+ \left ( {{\rm e}^{{\it \_Z}}} \right ) ^{2} \right ) +10\,{\it \_C1}-10\,{\it \_Z}-10\,x \right ) }} \right \}$
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