\[ y'(x)=-\frac {216 y(x) \left (-2 y(x)^4-3 y(x)^3-6 y(x)^2-6 y(x)+6 x+6\right )}{216 x^3-216 x^2 y(x)^4-324 x^2 y(x)^3-648 x^2 y(x)^2-648 x^2 y(x)-8 y(x)^{12}-36 y(x)^{11}-126 y(x)^{10}-315 y(x)^9+72 x y(x)^8-18 y(x)^8+216 x y(x)^7+594 y(x)^7+594 x y(x)^6+2484 y(x)^6+1080 x y(x)^5+4428 y(x)^5-432 x y(x)^4+2808 y(x)^4-648 x y(x)^3+1728 y(x)^3-1944 x y(x)^2-1296 y(x)^2-1296 x y(x)-1296 y(x)} \] ✓ Mathematica : cpu = 0.637253 (sec), leaf count = 66
DSolve[Derivative[1][y][x] == (-216*y[x]*(6 + 6*x - 6*y[x] - 6*y[x]^2 - 3*y[x]^3 - 2*y[x]^4))/(216*x^3 - 1296*y[x] - 1296*x*y[x] - 648*x^2*y[x] - 1296*y[x]^2 - 1944*x*y[x]^2 - 648*x^2*y[x]^2 + 1728*y[x]^3 - 648*x*y[x]^3 - 324*x^2*y[x]^3 + 2808*y[x]^4 - 432*x*y[x]^4 - 216*x^2*y[x]^4 + 4428*y[x]^5 + 1080*x*y[x]^5 + 2484*y[x]^6 + 594*x*y[x]^6 + 594*y[x]^7 + 216*x*y[x]^7 - 18*y[x]^8 + 72*x*y[x]^8 - 315*y[x]^9 - 126*y[x]^10 - 36*y[x]^11 - 8*y[x]^12),y[x],x]
\[\text {Solve}\left [\frac {36 \left (2 y(x)^4+3 y(x)^3+6 y(x)^2+6 y(x)-6 x-3\right )}{\left (y(x) \left (2 y(x)^3+3 y(x)^2+6 y(x)+6\right )-6 x\right )^2}+\log (y(x))=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.678 (sec), leaf count = 181
dsolve(diff(y(x),x) = -216*y(x)*(-2*y(x)^4-3*y(x)^3-6*y(x)^2-6*y(x)+6*x+6)/(1728*y(x)^3-1296*y(x)^2-1296*y(x)-1944*x*y(x)^2-1296*x*y(x)-648*x^2*y(x)-315*y(x)^9-8*y(x)^12-36*y(x)^11-126*y(x)^10+594*y(x)^7-18*y(x)^8+72*y(x)^8*x+216*y(x)^7*x+1080*y(x)^5*x+2484*y(x)^6+594*x*y(x)^6-216*x^2*y(x)^4+4428*y(x)^5-432*x*y(x)^4-648*x^2*y(x)^2-324*x^2*y(x)^3-648*x*y(x)^3+2808*y(x)^4+216*x^3),y(x))
\[\frac {-6 \sqrt {3 \ln \left (y \left (x \right )\right )-3 c_{1}+9}+\left (2 y \left (x \right )^{4}+3 y \left (x \right )^{3}+6 y \left (x \right )^{2}-6 x +6 y \left (x \right )\right ) \ln \left (y \left (x \right )\right )-2 c_{1} y \left (x \right )^{4}-3 c_{1} y \left (x \right )^{3}-6 c_{1} y \left (x \right )^{2}+6 c_{1} x -6 c_{1} y \left (x \right )+18}{6 c_{1}-6 \ln \left (y \left (x \right )\right )} = 0\]