\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac {1}{x} \left ( y \left ( x \right ) -\ln \left ( {\frac {1+x}{x-1}} \right ) {x}^{3}+\ln \left ( {\frac {1+x}{x-1}} \right ) x \left ( y \left ( x \right ) \right ) ^{2} \right ) }=0} \]
Mathematica: cpu = 0.064008 (sec), leaf count = 130 \[ \left \{\left \{y(x)\to \frac {-x^2 (x+1)^{x^2} e^{2 c_1+2 x}+x (x+1)^{x^2} e^{2 c_1+2 x}-x^2 (x-1)^{x^2}-x (x-1)^{x^2}}{-(x+1)^{x^2} e^{2 c_1+2 x}+x (x+1)^{x^2} e^{2 c_1+2 x}-x (x-1)^{x^2}-(x-1)^{x^2}}\right \}\right \} \]
Maple: cpu = 0.063 (sec), leaf count = 39 \[ \left \{ y \left ( x \right ) =-\tanh \left ( {\frac {{x}^{2}}{2}\ln \left ( {\frac {1+x}{x-1}} \right ) }-{\frac {1}{2}\ln \left ( {\frac { 1+x}{x-1}} \right ) }+{\it \_C1}+x-1 \right ) x \right \} \]