\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac {1}{\ln \left ( \left ( x-1 \right ) ^{-1} \right ) } \left ( 2\,x\ln \left ( \left ( x-1 \right ) ^{-1} \right ) -\coth \left ( {\frac {1+x}{x-1}} \right ) +\coth \left ( {\frac {1+x}{x-1}} \right ) \left ( y \left ( x \right ) \right ) ^{2}-2\,\coth \left ( {\frac {1+x}{x-1}} \right ) {x}^{2}y \left ( x \right ) +\coth \left ( {\frac {1+x}{x-1}} \right ) {x}^{4} \right ) }=0} \]
Mathematica: cpu = 1267.680975 (sec), leaf count = 95 \[ \left \{\left \{y(x)\to \frac {\exp \left (\int _1^x \frac {2 \coth \left (\frac {K[5]}{K[5]-1}+\frac {1}{K[5]-1}\right )}{\log \left (\frac {1}{K[5]-1}\right )} \, dK[5]\right )}{c_1-\frac {1}{2} \exp \left (\text {Integrate}\left [\frac {2 \coth \left (\frac {K[5]}{K[5]-1}+\frac {1}{K[5]-1}\right )}{\log \left (\frac {1}{K[5]-1}\right )},\{K[5],1,x\},\text {Assumptions}\to \text {True}\right ]\right )}+x^2+1\right \}\right \} \]
Maple: cpu = 0 (sec), leaf count = 0 \[ \text {hanged} \]