\[ y'(x)=\frac {1}{2} \sqrt {x} \left (2 F\left (y(x)-\frac {x^3}{6}\right )+x^{3/2}\right ) \] ✓ Mathematica : cpu = 0.224113 (sec), leaf count = 123
\[\text {Solve}\left [\int _1^{y(x)}-\frac {F\left (K[2]-\frac {x^3}{6}\right ) \int _1^x-\frac {K[1]^2 F'\left (K[2]-\frac {K[1]^3}{6}\right )}{2 F\left (K[2]-\frac {K[1]^3}{6}\right )^2}dK[1]+1}{F\left (K[2]-\frac {x^3}{6}\right )}dK[2]+\int _1^x\left (\frac {K[1]^2}{2 F\left (y(x)-\frac {K[1]^3}{6}\right )}+\sqrt {K[1]}\right )dK[1]=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.224 (sec), leaf count = 29
\[ \left \{ \int _{{\it \_b}}^{y \left ( x \right ) }\! \left ( F \left ( {\it \_a}-{\frac {{x}^{3}}{6}} \right ) \right ) ^{-1}\,{\rm d}{\it \_a}-{\frac {2}{3}{x}^{{\frac {3}{2}}}}-{\it \_C1}=0 \right \} \]