\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac { \left ( -256\,a{x}^{2}+512+512\, \left ( y \left ( x \right ) \right ) ^{2}+128\,y \left ( x \right ) a{x}^{4}+8\,{a}^{2}{x}^{8}+512\, \left ( y \left ( x \right ) \right ) ^{3}+192\,{x}^{4}a \left ( y \left ( x \right ) \right ) ^{2}+24\,y \left ( x \right ) {a}^{2}{x}^{8}+{a}^{3}{x}^{12} \right ) x}{512}}=0} \]
Mathematica: cpu = 0.067509 (sec), leaf count = 101 \[ \text {Solve}\left [-\frac {29}{3} \text {RootSum}\left [-29 \text {$\#$1}^3+3 \sqrt [3]{29} \text {$\#$1}-29\& ,\frac {\log \left (\frac {\frac {1}{8} \left (3 a x^5+8 x\right )+3 x y(x)}{\sqrt [3]{29} \sqrt [3]{x^3}}-\text {$\#$1}\right )}{\sqrt [3]{29}-29 \text {$\#$1}^2}\& \right ]=c_1+\frac {1}{18} 29^{2/3} \left (x^3\right )^{2/3},y(x)\right ] \]
Maple: cpu = 0.047 (sec), leaf count = 40 \[ \left \{ y \left ( x \right ) =-{\frac {a{x}^{4}}{8}}-{\frac {1}{3}}+{ \frac {29\,{\it RootOf} \left ( {x}^{2}-162\,\int ^{{\it \_Z}}\! \left ( 841\,{{\it \_a}}^{3}-27\,{\it \_a}+27 \right ) ^{-1}{d{\it \_a} }+6\,{\it \_C1} \right ) }{9}} \right \} \]