2.618   ODE No. 618

\[ y'(x)=\frac {(y(x)+1) (x (y(x)-\log (y(x)+1)-\log (x))+1)}{x y(x)} \] Mathematica : cpu = 0.210125 (sec), leaf count = 25


\[\left \{\left \{y(x)\to -1-W\left (-\frac {e^{-1+c_1 e^x}}{x}\right )\right \}\right \}\] Maple : cpu = 0.549 (sec), leaf count = 34


\[y \relax (x ) = \frac {{\mathrm e}^{-\LambertW \left (-\frac {{\mathrm e}^{c_{1} {\mathrm e}^{x}-1}}{x}\right )+c_{1} {\mathrm e}^{x}-1}-x}{x}\]