\[
\boxed{
{\frac {\rm d}{{\rm d}x}}y \left( x \right) =1/2\, \left( -\sqrt {a}{x}^{3}+2\,\sqrt {a{x}^{4}+8\,y \left( x \right) }+2\,{x}^{2}\sqrt {a{x}^{4}+8\,y \left( x \right) }+2\,{x}^{3}\sqrt {a{x}^{4}+8\,y \left( x \right) } \right) \sqrt {a}=0}
\]