\[ y'(x)=\frac {F\left (-\frac {2 x^3}{5}+y(x)-2 \sqrt {x}\right )+\frac {6 x^3}{5}+\sqrt {x}}{x} \] ✓ Mathematica : cpu = 463.993 (sec), leaf count = 238
\[\text {Solve}\left [\int _1^{y(x)} -\frac {F\left (K[2]-\frac {2 x^3}{5}-2 \sqrt {x}\right ) \int _1^x \left (-\frac {6 K[1]^2 F'\left (-\frac {2}{5} K[1]^3-2 \sqrt {K[1]}+K[2]\right )}{5 F\left (-\frac {2}{5} K[1]^3-2 \sqrt {K[1]}+K[2]\right )^2}-\frac {F'\left (-\frac {2}{5} K[1]^3-2 \sqrt {K[1]}+K[2]\right )}{\sqrt {K[1]} F\left (-\frac {2}{5} K[1]^3-2 \sqrt {K[1]}+K[2]\right )^2}\right ) \, dK[1]+1}{F\left (K[2]-\frac {2 x^3}{5}-2 \sqrt {x}\right )} \, dK[2]+\int _1^x \left (\frac {6 K[1]^2}{5 F\left (-\frac {2}{5} K[1]^3-2 \sqrt {K[1]}+y(x)\right )}+\frac {1}{\sqrt {K[1]} F\left (-\frac {2}{5} K[1]^3-2 \sqrt {K[1]}+y(x)\right )}+\frac {1}{K[1]}\right ) \, dK[1]=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.199 (sec), leaf count = 33
\[ \left \{ \int _{{\it \_b}}^{y \left ( x \right ) }\! \left ( F \left ( {\it \_a}-{\frac {2\,{x}^{3}}{5}}-2\,\sqrt {x} \right ) \right ) ^{-1}\,{\rm d}{\it \_a}-\ln \left ( x \right ) -{\it \_C1}=0 \right \} \]