\[
\boxed{
{\frac {\rm d}{{\rm d}x}}y \left( x \right) =-{\frac {-xy \left( x \right) -y \left( x \right) +{x}^{5}\sqrt { \left( y \left( x \right)  \right) ^{2}+{x}^{2}}-{x}^{4}\sqrt { \left( y \left( x \right)  \right) ^{2}+{x}^{2}}y \left( x \right) }{x \left( 1+x \right) }}=0}
\]