\[
\boxed{
{\frac {\rm d}{{\rm d}x}}y \left( x \right) ={\frac {2\,{x}^{2}\cosh \left(  \left( x-1 \right) ^{-1} \right) -2\,x\cosh \left(  \left( x-1 \right) ^{-1} \right) -1+ \left( y \left( x \right)  \right) ^{2}-2\,{x}^{2}y \left( x \right) +{x}^{4}-x+x \left( y \left( x \right)  \right) ^{2}-2\,{x}^{3}y \left( x \right) +{x}^{5}}{ \left( x-1 \right) \cosh \left(  \left( x-1 \right) ^{-1} \right) }}=0}
\]