\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) =-1296\,{\frac {y \left ( x \right ) }{216-432\,xy \left ( x \right ) -648\,{x}^{2}y \left ( x \right ) +216\,x \left ( y \left ( x \right ) \right ) ^{2}-1296\,y \left ( x \right ) +216\,{x}^{3}+216\,{x}^{2}-2376\, \left ( y \left ( x \right ) \right ) ^{2}-1728\, \left ( y \left ( x \right ) \right ) ^{3}+1080\,x \left ( y \left ( x \right ) \right ) ^{3}-324\,{x}^{2} \left ( y \left ( x \right ) \right ) ^{3}-648\,{x}^{2} \left ( y \left ( x \right ) \right ) ^{2}-1944\, \left ( y \left ( x \right ) \right ) ^{4}-126\, \left ( y \left ( x \right ) \right ) ^{10}-315\, \left ( y \left ( x \right ) \right ) ^{9}-8\, \left ( y \left ( x \right ) \right ) ^{12}-36\, \left ( y \left ( x \right ) \right ) ^{11}-846\, \left ( y \left ( x \right ) \right ) ^{7}+72\, \left ( y \left ( x \right ) \right ) ^{8}x+216\, \left ( y \left ( x \right ) \right ) ^{7}x+1080\, \left ( y \left ( x \right ) \right ) ^{5}x-570\, \left ( y \left ( x \right ) \right ) ^{8}+594\,x \left ( y \left ( x \right ) \right ) ^{6}-216\,{x}^{2} \left ( y \left ( x \right ) \right ) ^{4}-882\, \left ( y \left ( x \right ) \right ) ^{6}+1152\,x \left ( y \left ( x \right ) \right ) ^{4}-612\, \left ( y \left ( x \right ) \right ) ^{5}}}=0} \]
Mathematica: cpu = 0.439556 (sec), leaf count = 292 \[ \text {Solve}\left [72 \text {RootSum}\left [-216 \text {$\#$1}^3+216 \text {$\#$1}^2 y(x)^4+324 \text {$\#$1}^2 y(x)^3+648 \text {$\#$1}^2 y(x)^2+648 \text {$\#$1}^2 y(x)-216 \text {$\#$1}^2-72 \text {$\#$1} y(x)^8-216 \text {$\#$1} y(x)^7-594 \text {$\#$1} y(x)^6-1080 \text {$\#$1} y(x)^5-1152 \text {$\#$1} y(x)^4-1080 \text {$\#$1} y(x)^3-216 \text {$\#$1} y(x)^2+432 \text {$\#$1} y(x)+8 y(x)^{12}+36 y(x)^{11}+126 y(x)^{10}+315 y(x)^9+570 y(x)^8+846 y(x)^7+882 y(x)^6+612 y(x)^5+216 y(x)^4-216 y(x)^3-216 y(x)^2-216\& ,\frac {\log (x-\text {$\#$1})}{36 \text {$\#$1}^2-24 \text {$\#$1} y(x)^4-36 \text {$\#$1} y(x)^3-72 \text {$\#$1} y(x)^2-72 \text {$\#$1} y(x)+24 \text {$\#$1}+4 y(x)^8+12 y(x)^7+33 y(x)^6+60 y(x)^5+64 y(x)^4+60 y(x)^3+12 y(x)^2-24 y(x)}\& \right ]+\log (y(x))=c_1,y(x)\right ] \]
Maple: cpu = 0.484 (sec), leaf count = 50 \[ \left \{ y \left ( x \right ) ={{\rm e}^{{\it RootOf} \left ( -{\it \_Z}- 6\,\int ^{x-1/3\, \left ( {{\rm e}^{{\it \_Z}}} \right ) ^{4}-1/2\, \left ( {{\rm e}^{{\it \_Z}}} \right ) ^{3}- \left ( {{\rm e}^{{\it \_Z} }} \right ) ^{2}-{{\rm e}^{{\it \_Z}}}}\! \left ( {{\it \_a}}^{3}+{{\it \_a}}^{2}+1 \right ) ^{-1}{d{\it \_a}}+{\it \_C1} \right ) }} \right \} \]