\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac {-128\,xy \left ( x \right ) -24\,{x}^{3}+32\,{x}^{2}-128\,x+512\, \left ( y \left ( x \right ) \right ) ^{3}+192\,{x}^{2} \left ( y \left ( x \right ) \right ) ^{2}-384\,x \left ( y \left ( x \right ) \right ) ^{2}+24\,y \left ( x \right ) {x}^{4}-96\,{x}^{3}y \left ( x \right ) +96\,{x}^{2}y \left ( x \right ) +{x}^{6}-6\,{x}^{5}+12\,{x}^{4}}{512\,y \left ( x \right ) +64\,{x}^{2}-128\,x+512}}=0} \]
Mathematica: cpu = 0.394550 (sec), leaf count = 53 \[ \text {Solve}\left [x-16 \text {RootSum}\left [6656 \text {$\#$1}^3-23 \text {$\#$1}-1\& ,\text {$\#$1} \log \left (79872 \text {$\#$1}^2-18304 \text {$\#$1}+181 x^2+1448 y(x)-362 x-184\right )\& \right ]=c_1,y(x)\right ] \]
Maple: cpu = 0.047 (sec), leaf count = 40 \[ \left \{ y \left ( x \right ) =-{\frac {{x}^{2}}{8}}+{\frac {x}{4}}+{ \it RootOf} \left ( -x+\int ^{{\it \_Z}}\!4\,{\frac {{\it \_a}+1}{4\,{{ \it \_a}}^{3}-{\it \_a}-1}}{d{\it \_a}}+{\it \_C1} \right ) \right \} \]