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