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