\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) =-216\,{\frac {y \left ( x \right ) \left ( -2\, \left ( y \left ( x \right ) \right ) ^{4}-3\, \left ( y \left ( x \right ) \right ) ^{3}-6\, \left ( y \left ( x \right ) \right ) ^{2}-6\,y \left ( x \right ) +6\,x+6 \right ) }{-1296\,xy \left ( x \right ) -648\,{x}^{2}y \left ( x \right ) -1944\,x \left ( y \left ( x \right ) \right ) ^{2}-1296\,y \left ( x \right ) +216\,{x}^{3}-1296\, \left ( y \left ( x \right ) \right ) ^{2}+1728\, \left ( y \left ( x \right ) \right ) ^{3}-648\,x \left ( y \left ( x \right ) \right ) ^{3}-324\,{x}^{2} \left ( y \left ( x \right ) \right ) ^{3}-648\,{x}^{2} \left ( y \left ( x \right ) \right ) ^{2}+2808\, \left ( y \left ( x \right ) \right ) ^{4}-126\, \left ( y \left ( x \right ) \right ) ^{10}-315\, \left ( y \left ( x \right ) \right ) ^{9}-8\, \left ( y \left ( x \right ) \right ) ^{12}-36\, \left ( y \left ( x \right ) \right ) ^{11}+594\, \left ( y \left ( x \right ) \right ) ^{7}+72\, \left ( y \left ( x \right ) \right ) ^{8}x+216\, \left ( y \left ( x \right ) \right ) ^{7}x+1080\, \left ( y \left ( x \right ) \right ) ^{5}x-18\, \left ( y \left ( x \right ) \right ) ^{8}+594\,x \left ( y \left ( x \right ) \right ) ^{6}-216\,{x}^{2} \left ( y \left ( x \right ) \right ) ^{4}+2484\, \left ( y \left ( x \right ) \right ) ^{6}-432\,x \left ( y \left ( x \right ) \right ) ^{4}+4428\, \left ( y \left ( x \right ) \right ) ^{5}}}=0} \]
Mathematica: cpu = 0.475060 (sec), leaf count = 66 \[ \text {Solve}\left [\frac {36 \left (2 y(x)^4+3 y(x)^3+6 y(x)^2+6 y(x)-6 x-3\right )}{\left (y(x) \left (2 y(x)^3+3 y(x)^2+6 y(x)+6\right )-6 x\right )^2}+\log (y(x))=c_1,y(x)\right ] \]
Maple: cpu = 0.562 (sec), leaf count = 183 \[ \left \{ x-{\frac {1}{-6\,{\it \_C1}+6\,\ln \left ( y \left ( x \right ) \right ) } \left ( 2\,\ln \left ( y \left ( x \right ) \right ) \left ( y \left ( x \right ) \right ) ^{4}-2\,{\it \_C1}\, \left ( y \left ( x \right ) \right ) ^{4}+3\,\ln \left ( y \left ( x \right ) \right ) \left ( y \left ( x \right ) \right ) ^{3}-3\,{\it \_C1}\, \left ( y \left ( x \right ) \right ) ^{3}+6\, \left ( y \left ( x \right ) \right ) ^{2}\ln \left ( y \left ( x \right ) \right ) -6\,{ \it \_C1}\, \left ( y \left ( x \right ) \right ) ^{2}+6\,y \left ( x \right ) \ln \left ( y \left ( x \right ) \right ) -6\,y \left ( x \right ) {\it \_C1}-6\,\sqrt {3\,\ln \left ( y \left ( x \right ) \right ) -3\,{\it \_C1}+9}+18 \right ) }=0,x-{\frac {1}{-6\,{\it \_C1}+ 6\,\ln \left ( y \left ( x \right ) \right ) } \left ( 2\,\ln \left ( y \left ( x \right ) \right ) \left ( y \left ( x \right ) \right ) ^{4}-2 \,{\it \_C1}\, \left ( y \left ( x \right ) \right ) ^{4}+3\,\ln \left ( y \left ( x \right ) \right ) \left ( y \left ( x \right ) \right ) ^{3}-3 \,{\it \_C1}\, \left ( y \left ( x \right ) \right ) ^{3}+6\, \left ( y \left ( x \right ) \right ) ^{2}\ln \left ( y \left ( x \right ) \right ) -6\,{\it \_C1}\, \left ( y \left ( x \right ) \right ) ^{2}+6\,y \left ( x \right ) \ln \left ( y \left ( x \right ) \right ) -6\,y \left ( x \right ) {\it \_C1}+6\,\sqrt {3\,\ln \left ( y \left ( x \right ) \right ) -3\,{\it \_C1}+9}+18 \right ) }=0 \right \} \]