\[ y'(x)=\frac {x^6-6 x^5+24 x^4 y(x)+12 x^4-96 x^3 y(x)-24 x^3+192 x^2 y(x)^2+96 x^2 y(x)+32 x^2-384 x y(x)^2-128 x y(x)+512 y(x)^3-128 x}{64 x^2+512 y(x)-128 x+512} \] ✓ Mathematica : cpu = 0.498528 (sec), leaf count = 53
DSolve[Derivative[1][y][x] == (-128*x + 32*x^2 - 24*x^3 + 12*x^4 - 6*x^5 + x^6 - 128*x*y[x] + 96*x^2*y[x] - 96*x^3*y[x] + 24*x^4*y[x] - 384*x*y[x]^2 + 192*x^2*y[x]^2 + 512*y[x]^3)/(512 - 128*x + 64*x^2 + 512*y[x]),y[x],x]
\[\text {Solve}\left [x-16 \text {RootSum}\left [6656 \text {$\#$1}^3-23 \text {$\#$1}-1\& ,\text {$\#$1} \log \left (79872 \text {$\#$1}^2-18304 \text {$\#$1}+181 x^2+1448 y(x)-362 x-184\right )\& \right ]=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.051 (sec), leaf count = 40
dsolve(diff(y(x),x) = (-128*x*y(x)-24*x^3+32*x^2-128*x+512*y(x)^3+192*x^2*y(x)^2-384*x*y(x)^2+24*y(x)*x^4-96*x^3*y(x)+96*x^2*y(x)+x^6-6*x^5+12*x^4)/(512*y(x)+64*x^2-128*x+512),y(x))
\[y \left (x \right ) = -\frac {x^{2}}{8}+\frac {x}{4}+\RootOf \left (-x +\int _{}^{\textit {\_Z}}\frac {4 \textit {\_a} +4}{4 \textit {\_a}^{3}-\textit {\_a} -1}d \textit {\_a} +c_{1}\right )\]