\[ y'(x)=\frac {F\left (-\frac {2 x^3}{5}+y(x)-2 \sqrt {x}\right )+\frac {6 x^3}{5}+\sqrt {x}}{x} \] ✓ Mathematica : cpu = 0.550474 (sec), leaf count = 241
DSolve[Derivative[1][y][x] == (Sqrt[x] + (6*x^3)/5 + F[-2*Sqrt[x] - (2*x^3)/5 + y[x]])/x,y[x],x]
\[\text {Solve}\left [\int _1^{y(x)}-\frac {F\left (-\frac {2 x^3}{5}-2 \sqrt {x}+K[2]\right ) \int _1^x\left (-\frac {6 F'\left (-\frac {2}{5} K[1]^3-2 \sqrt {K[1]}+K[2]\right ) K[1]^2}{5 F\left (-\frac {2}{5} K[1]^3-2 \sqrt {K[1]}+K[2]\right )^2}-\frac {F'\left (-\frac {2}{5} K[1]^3-2 \sqrt {K[1]}+K[2]\right )}{F\left (-\frac {2}{5} K[1]^3-2 \sqrt {K[1]}+K[2]\right )^2 \sqrt {K[1]}}\right )dK[1]+1}{F\left (-\frac {2 x^3}{5}-2 \sqrt {x}+K[2]\right )}dK[2]+\int _1^x\left (\frac {6 K[1]^2}{5 F\left (-\frac {2}{5} K[1]^3-2 \sqrt {K[1]}+y(x)\right )}+\frac {1}{F\left (-\frac {2}{5} K[1]^3-2 \sqrt {K[1]}+y(x)\right ) \sqrt {K[1]}}+\frac {1}{K[1]}\right )dK[1]=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.182 (sec), leaf count = 33
dsolve(diff(y(x),x) = 1/5*(6*x^3+5*x^(1/2)+5*F(y(x)-2/5*x^3-2*x^(1/2)))/x,y(x))
\[\int _{\textit {\_b}}^{y \left (x \right )}\frac {1}{F \left (\textit {\_a} -\frac {2 x^{3}}{5}-2 \sqrt {x}\right )}d \textit {\_a} -\ln \left (x \right )-c_{1} = 0\]