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