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