\[ y'(x)=\frac {6 y(x)}{-F\left (-\frac {1}{3} y(x)^4-\frac {y(x)^3}{2}-y(x)^2-y(x)+x\right )+8 y(x)^4+9 y(x)^3+12 y(x)^2+6 y(x)} \] ✓ Mathematica : cpu = 270.489 (sec), leaf count = 195
\[\text {Solve}\left [c_1=\int _1^{y(x)} \left (-\int _1^x \frac {\left (8 K[2]^3+9 K[2]^2+12 K[2]+6\right ) F'\left (K[1]-\frac {1}{6} K[2] \left (2 K[2]^3+3 K[2]^2+6 K[2]+6\right )\right )}{F\left (K[1]-\frac {1}{6} K[2] \left (2 K[2]^3+3 K[2]^2+6 K[2]+6\right )\right )^2} \, dK[1]-\frac {8 K[2]^3+9 K[2]^2+12 K[2]+6}{F\left (x-\frac {1}{6} K[2] \left (2 K[2]^3+3 K[2]^2+6 K[2]+6\right )\right )}+\frac {1}{K[2]}\right ) \, dK[2]+\int _1^x \frac {6}{F\left (K[1]-\frac {1}{3} y(x)^4-\frac {y(x)^3}{2}-y(x)^2-y(x)\right )} \, dK[1],y(x)\right ]\]
✓ Maple : cpu = 0.535 (sec), leaf count = 81
\[ \left \{ \int _{{\it \_b}}^{y \left ( x \right ) }\!{\frac {1}{{\it \_a}} \left ( -8\,{{\it \_a}}^{4}-9\,{{\it \_a}}^{3}-12\,{{\it \_a}}^{2}+F \left ( -{\frac {{{\it \_a}}^{4}}{3}}-{\frac {{{\it \_a}}^{3}}{2}}-{{\it \_a}}^{2}-{\it \_a}+x \right ) -6\,{\it \_a} \right ) \left ( F \left ( -{\frac {{{\it \_a}}^{4}}{3}}-{\frac {{{\it \_a}}^{3}}{2}}-{{\it \_a}}^{2}-{\it \_a}+x \right ) \right ) ^{-1}}\,{\rm d}{\it \_a}-{\it \_C1}=0 \right \} \]