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