\[ y'(x)=\frac {x^3 \left (-\log \left (\frac {x+1}{x-1}\right )\right )+y(x)+x y(x)^2 \log \left (\frac {x+1}{x-1}\right )}{x} \] ✓ Mathematica : cpu = 0.1661 (sec), leaf count = 130
DSolve[Derivative[1][y][x] == (-(x^3*Log[(1 + x)/(-1 + x)]) + y[x] + x*Log[(1 + x)/(-1 + x)]*y[x]^2)/x,y[x],x]
\[\left \{\left \{y(x)\to \frac {-x^2 (x-1)^{x^2}-x (x-1)^{x^2}-x^2 (x+1)^{x^2} e^{2 x+2 c_1}+x (x+1)^{x^2} e^{2 x+2 c_1}}{-x (x-1)^{x^2}-(x-1)^{x^2}-(x+1)^{x^2} e^{2 x+2 c_1}+x (x+1)^{x^2} e^{2 x+2 c_1}}\right \}\right \}\] ✓ Maple : cpu = 0.125 (sec), leaf count = 39
dsolve(diff(y(x),x) = (y(x)-ln((1+x)/(x-1))*x^3+ln((1+x)/(x-1))*x*y(x)^2)/x,y(x))
\[y \left (x \right ) = -\tanh \left (\frac {x^{2} \ln \left (\frac {1+x}{x -1}\right )}{2}-\frac {\ln \left (\frac {1+x}{x -1}\right )}{2}+c_{1}+x -1\right ) x\]