\[ y'(x)=\frac {1}{2} \sqrt {x} \left (2 F\left (y(x)-\frac {x^3}{6}\right )+x^{3/2}\right ) \] ✓ Mathematica : cpu = 0.298573 (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 = 0.119 (sec), leaf count = 29
\[\left \{-\frac {2 x^{\frac {3}{2}}}{3}-c_{1}+\int _{\textit {\_b}}^{y \left (x \right )}\frac {1}{F \left (-\frac {x^{3}}{6}+\textit {\_a} \right )}d \textit {\_a} = 0\right \}\]