\[
\boxed{
{\frac {\rm d}{{\rm d}x}}y \left( x \right) ={\frac {1}{\ln  \left(  \left( x-1 \right) ^{-1} \right) } \left( 2\,x\ln  \left(  \left( x-1 \right) ^{-1} \right) -\coth \left( {\frac {1+x}{x-1}} \right) +\coth \left( {\frac {1+x}{x-1}} \right)  \left( y \left( x \right)  \right) ^{2}-2\,\coth \left( {\frac {1+x}{x-1}} \right) {x}^{2}y \left( x \right) +\coth \left( {\frac {1+x}{x-1}} \right) {x}^{4} \right) }=0}
\]