\[
\boxed{
{\frac {\rm d}{{\rm d}x}}y \left( x \right) =1/2\,{\frac {x+1+2\,{x}^{6}\sqrt {4\,{x}^{2}y \left( x \right) +1}}{{x}^{3} \left( 1+x \right) }}=0}
\]