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