\[
\boxed{
{\frac {\rm d}{{\rm d}x}}y \left( x \right) ={\frac { \left( -256\,a{x}^{2}+512+512\, \left( y \left( x \right)  \right) ^{2}+128\,y \left( x \right) a{x}^{4}+8\,{a}^{2}{x}^{8}+512\, \left( y \left( x \right)  \right) ^{3}+192\,{x}^{4}a \left( y \left( x \right)  \right) ^{2}+24\,y \left( x \right) {a}^{2}{x}^{8}+{a}^{3}{x}^{12} \right) x}{512}}=0}
\]