\[
\boxed{
{\frac {\rm d}{{\rm d}x}}y \left( x \right) =1/2\,{\frac {{x}^{2}+2\,x+1+2\,{x}^{3}\sqrt {{x}^{2}+2\,x+1-4\,y \left( x \right) }}{1+x}}=0}
\]