\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac {-32\,xy \left ( x \right ) -8\,{x}^{3}-16\,a{x}^{2}-32\,x+64\, \left ( y \left ( x \right ) \right ) ^{3}+48\,{x}^{2} \left ( y \left ( x \right ) \right ) ^{2}+96\,ax \left ( y \left ( x \right ) \right ) ^{2}+12\,y \left ( x \right ) {x}^{4}+48\,y \left ( x \right ) a{x}^{3}+48\,{a}^{2}{x}^{2}y \left ( x \right ) +{x}^{6}+6\,{x}^{5}a+12\,{a}^{2}{x}^{4}+8\,{a}^{3}{x}^{3}}{64\,y \left ( x \right ) +16\,{x}^{2}+32\,ax+64}}=0} \]
Mathematica: cpu = 1.213154 (sec), leaf count = 213 \[ \text {Solve}\left [x-4 \text {RootSum}\left [\text {$\#$1}^6+6 \text {$\#$1}^5 a+12 \text {$\#$1}^4 a^2+12 \text {$\#$1}^4 y(x)+8 \text {$\#$1}^3 a^3+48 \text {$\#$1}^3 a y(x)+48 \text {$\#$1}^2 a^2 y(x)+8 \text {$\#$1}^2 a+48 \text {$\#$1}^2 y(x)^2+16 \text {$\#$1} a^2+96 \text {$\#$1} a y(x)^2+32 a y(x)+32 a+64 y(x)^3\& ,\frac {\text {$\#$1}^2 \log (x-\text {$\#$1})+2 \text {$\#$1} a \log (x-\text {$\#$1})+4 y(x) \log (x-\text {$\#$1})+4 \log (x-\text {$\#$1})}{3 \text {$\#$1}^4+12 \text {$\#$1}^3 a+12 \text {$\#$1}^2 a^2+24 \text {$\#$1}^2 y(x)+48 \text {$\#$1} a y(x)+8 a+48 y(x)^2}\& \right ]=c_1,y(x)\right ] \]
Maple: cpu = 0.047 (sec), leaf count = 41 \[ \left \{ y \left ( x \right ) =-{\frac {{x}^{2}}{4}}-{\frac {ax}{2}}+{ \it RootOf} \left ( -x+\int ^{{\it \_Z}}\!2\,{\frac {{\it \_a}+1}{2\,{{ \it \_a}}^{3}+{\it \_a}\,a+a}}{d{\it \_a}}+{\it \_C1} \right ) \right \} \]