\[ y'(x)=\frac {1}{512} x \left (a^3 x^{12}+24 a^2 x^8 y(x)+8 a^2 x^8+192 a x^4 y(x)^2+128 a x^4 y(x)-256 a x^2+512 y(x)^3+512 y(x)^2+512\right ) \] ✓ Mathematica : cpu = 0.236333 (sec), leaf count = 101
DSolve[Derivative[1][y][x] == (x*(512 - 256*a*x^2 + 8*a^2*x^8 + a^3*x^12 + 128*a*x^4*y[x] + 24*a^2*x^8*y[x] + 512*y[x]^2 + 192*a*x^4*y[x]^2 + 512*y[x]^3))/512,y[x],x]
\[\text {Solve}\left [-\frac {29}{3} \text {RootSum}\left [-29 \text {$\#$1}^3+3 \sqrt [3]{29} \text {$\#$1}-29\& ,\frac {\log \left (\frac {\frac {1}{8} \left (3 a x^5+8 x\right )+3 x y(x)}{\sqrt [3]{29} \sqrt [3]{x^3}}-\text {$\#$1}\right )}{\sqrt [3]{29}-29 \text {$\#$1}^2}\& \right ]=\frac {1}{18} 29^{2/3} \left (x^3\right )^{2/3}+c_1,y(x)\right ]\] ✓ Maple : cpu = 0.048 (sec), leaf count = 40
dsolve(diff(y(x),x) = 1/512*(-256*a*x^2+512+512*y(x)^2+128*y(x)*a*x^4+8*a^2*x^8+512*y(x)^3+192*x^4*a*y(x)^2+24*y(x)*a^2*x^8+a^3*x^12)*x,y(x))
\[y \left (x \right ) = -\frac {a \,x^{4}}{8}-\frac {1}{3}+\frac {29 \RootOf \left (x^{2}-162 \left (\int _{}^{\textit {\_Z}}\frac {1}{841 \textit {\_a}^{3}-27 \textit {\_a} +27}d \textit {\_a} \right )+6 c_{1}\right )}{9}\]