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