\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) =6\,{\frac {y \left ( x \right ) }{8\, \left ( y \left ( x \right ) \right ) ^{4}+9\, \left ( y \left ( x \right ) \right ) ^{3}+12\, \left ( y \left ( x \right ) \right ) ^{2}+6\,y \left ( x \right ) -F \left ( -1/3\, \left ( y \left ( x \right ) \right ) ^{4}-1/2\, \left ( y \left ( x \right ) \right ) ^{3}- \left ( y \left ( x \right ) \right ) ^{2}-y \left ( x \right ) +x \right ) }}=0} \]
Mathematica: cpu = 60.581193 (sec), leaf count = 327 \[ \text {Solve}\left [\int _1^{y(x)} \left (-\frac {F\left (-\frac {1}{3} K[2]^4-\frac {K[2]^3}{2}-K[2]^2-K[2]+x\right ) \int _1^x -\frac {6 \left (-\frac {4}{3} K[2]^3-\frac {3 K[2]^2}{2}-2 K[2]-1\right ) F'\left (-\frac {1}{3} K[2]^4-\frac {K[2]^3}{2}-K[2]^2-K[2]+K[1]\right )}{F\left (-\frac {1}{3} K[2]^4-\frac {K[2]^3}{2}-K[2]^2-K[2]+K[1]\right )^2} \, dK[1]+6}{F\left (-\frac {1}{3} K[2]^4-\frac {K[2]^3}{2}-K[2]^2-K[2]+x\right )}-\frac {8 K[2]^3}{F\left (-\frac {1}{3} K[2]^4-\frac {K[2]^3}{2}-K[2]^2-K[2]+x\right )}-\frac {9 K[2]^2}{F\left (-\frac {1}{3} K[2]^4-\frac {K[2]^3}{2}-K[2]^2-K[2]+x\right )}-\frac {12 K[2]}{F\left (-\frac {1}{3} K[2]^4-\frac {K[2]^3}{2}-K[2]^2-K[2]+x\right )}+\frac {1}{K[2]}\right ) \, dK[2]+\int _1^x \frac {6}{F\left (K[1]-\frac {1}{3} y(x)^4-\frac {y(x)^3}{2}-y(x)^2-y(x)\right )} \, dK[1]=c_1,y(x)\right ] \]
Maple: cpu = 0.359 (sec), leaf count = 81 \[ \left \{ \int _{{\it \_b}}^{y \left ( x \right ) }\!{\frac {1}{{\it \_a}} \left ( -8\,{{\it \_a}}^{4}-9\,{{\it \_a}}^{3}-12\,{{\it \_a}}^{2}+F \left ( -{\frac {{{\it \_a}}^{4}}{3}}-{\frac {{{\it \_a}}^{3}}{2}}-{{ \it \_a}}^{2}-{\it \_a}+x \right ) -6\,{\it \_a} \right ) \left ( F \left ( -{\frac {{{\it \_a}}^{4}}{3}}-{\frac {{{\it \_a}}^{3}}{2}}-{{ \it \_a}}^{2}-{\it \_a}+x \right ) \right ) ^{-1}}\,{\rm d}{\it \_a}-{ \it \_C1}=0 \right \} \]