\[
\boxed{
{\frac {\rm d}{{\rm d}x}}y \left( x \right) =2\,{\frac {ax}{-{x}^{3}y \left( x \right) +2\,a{x}^{3}+2\,a \left( y \left( x \right)  \right) ^{4}{x}^{3}-16\, \left( y \left( x \right)  \right) ^{2}{a}^{2}{x}^{2}+32\,{a}^{3}x+2\,a \left( y \left( x \right)  \right) ^{6}{x}^{3}-24\, \left( y \left( x \right)  \right) ^{4}{a}^{2}{x}^{2}+96\, \left( y \left( x \right)  \right) ^{2}x{a}^{3}-128\,{a}^{4}}}=0}
\]