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