\[ y'(x)=\frac {8 a^3 x^3+12 a^2 x^4+48 a^2 x^2 y(x)+6 a x^5+48 a x^3 y(x)-16 a x^2+96 a x y(x)^2+x^6+12 x^4 y(x)-8 x^3+48 x^2 y(x)^2-32 x y(x)+64 y(x)^3-32 x}{32 a x+16 x^2+64 y(x)+64} \] ✓ Mathematica : cpu = 1.22802 (sec), leaf count = 213
DSolve[Derivative[1][y][x] == (-32*x - 16*a*x^2 - 8*x^3 + 8*a^3*x^3 + 12*a^2*x^4 + 6*a*x^5 + x^6 - 32*x*y[x] + 48*a^2*x^2*y[x] + 48*a*x^3*y[x] + 12*x^4*y[x] + 96*a*x*y[x]^2 + 48*x^2*y[x]^2 + 64*y[x]^3)/(64 + 32*a*x + 16*x^2 + 64*y[x]),y[x],x]
\[\text {Solve}\left [x-4 \text {RootSum}\left [\text {$\#$1}^6+6 \text {$\#$1}^5 a+12 \text {$\#$1}^4 a^2+12 \text {$\#$1}^4 y(x)+8 \text {$\#$1}^3 a^3+48 \text {$\#$1}^3 a y(x)+48 \text {$\#$1}^2 a^2 y(x)+8 \text {$\#$1}^2 a+48 \text {$\#$1}^2 y(x)^2+16 \text {$\#$1} a^2+96 \text {$\#$1} a y(x)^2+32 a y(x)+32 a+64 y(x)^3\& ,\frac {\text {$\#$1}^2 \log (x-\text {$\#$1})+2 \text {$\#$1} a \log (x-\text {$\#$1})+4 y(x) \log (x-\text {$\#$1})+4 \log (x-\text {$\#$1})}{3 \text {$\#$1}^4+12 \text {$\#$1}^3 a+12 \text {$\#$1}^2 a^2+24 \text {$\#$1}^2 y(x)+48 \text {$\#$1} a y(x)+8 a+48 y(x)^2}\& \right ]=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.058 (sec), leaf count = 41
dsolve(diff(y(x),x) = (-32*x*y(x)-8*x^3-16*a*x^2-32*x+64*y(x)^3+48*x^2*y(x)^2+96*a*x*y(x)^2+12*y(x)*x^4+48*y(x)*a*x^3+48*a^2*x^2*y(x)+x^6+6*x^5*a+12*a^2*x^4+8*a^3*x^3)/(64*y(x)+16*x^2+32*a*x+64),y(x))
\[y \left (x \right ) = -\frac {x^{2}}{4}-\frac {a x}{2}+\RootOf \left (-x +\int _{}^{\textit {\_Z}}\frac {2 \textit {\_a} +2}{2 \textit {\_a}^{3}+\textit {\_a} a +a}d \textit {\_a} +c_{1}\right )\]