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