2.687   ODE No. 687

\[ y'(x)=\frac {x^3 \left (-\log \left (\frac {x+1}{x-1}\right )\right )+y(x)+x y(x)^2 \log \left (\frac {x+1}{x-1}\right )}{x} \] Mathematica : cpu = 0.1661 (sec), leaf count = 130


\[\left \{\left \{y(x)\to \frac {-x^2 (x-1)^{x^2}-x (x-1)^{x^2}-x^2 (x+1)^{x^2} e^{2 x+2 c_1}+x (x+1)^{x^2} e^{2 x+2 c_1}}{-x (x-1)^{x^2}-(x-1)^{x^2}-(x+1)^{x^2} e^{2 x+2 c_1}+x (x+1)^{x^2} e^{2 x+2 c_1}}\right \}\right \}\] Maple : cpu = 0.125 (sec), leaf count = 39


\[y \relax (x ) = -\tanh \left (\frac {x^{2} \ln \left (\frac {1+x}{x -1}\right )}{2}-\frac {\ln \left (\frac {1+x}{x -1}\right )}{2}+c_{1}+x -1\right ) x\]