\[ y'(x)=\frac {8 a^3 x^3+12 a^2 x^4+48 a^2 x^2 y(x)+6 a x^5+48 a x^3 y(x)-16 a x^2+96 a x y(x)^2+x^6+12 x^4 y(x)-8 x^3+48 x^2 y(x)^2-32 x y(x)+64 y(x)^3-32 x}{32 a x+16 x^2+64 y(x)+64} \] ✓ Mathematica : cpu = 1.55542 (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 = 0.085 (sec), leaf count = 41
\[ \left \{ y \left ( x \right ) =-{\frac {{x}^{2}}{4}}-{\frac {ax}{2}}+{\it RootOf} \left ( -x+\int ^{{\it \_Z}}\!2\,{\frac {{\it \_a}+1}{2\,{{\it \_a}}^{3}+{\it \_a}\,a+a}}{d{\it \_a}}+{\it \_C1} \right ) \right \} \]