ODE No. 632

\[ y'(x)=\frac {e^x}{e^{-x} y(x)+1} \] Mathematica : cpu = 0.219493 (sec), leaf count = 65

DSolve[Derivative[1][y][x] == E^x/(1 + y[x]/E^x),y[x],x]
 

\[\text {Solve}\left [\frac {1}{2} \log \left (-e^{-2 x} y(x)^2-e^{-x} y(x)+1\right )+x=\frac {\tanh ^{-1}\left (\frac {y(x)+3 e^x}{\sqrt {5} \left (y(x)+e^x\right )}\right )}{\sqrt {5}}+c_1,y(x)\right ]\] Maple : cpu = 0.341 (sec), leaf count = 54

dsolve(diff(y(x),x) = 1/(y(x)*exp(-x)+1)*exp(x),y(x))
 

\[x -\frac {\sqrt {5}\, \arctanh \left (\frac {2 y \left (x \right ) \sqrt {5}\, {\mathrm e}^{-x}}{5}+\frac {\sqrt {5}}{5}\right )}{5}+\frac {\ln \left (y \left (x \right )^{2} {\mathrm e}^{-2 x}+y \left (x \right ) {\mathrm e}^{-x}-1\right )}{2}-c_{1} = 0\]