\[
\boxed{
{\frac {\rm d}{{\rm d}x}}y \left( x \right) ={\frac {y \left( x \right) \ln  \left( x-1 \right) +{{\rm e}^{1+x}}{x}^{3}+7\,{{\rm e}^{1+x}}x \left( y \left( x \right)  \right) ^{2}}{\ln  \left( x-1 \right) x}}=0}
\]