ODE No. 585

$$y^{\prime }(x)=y(x)F(\log (\log (y(x)))-\log (x))$$ ✓ Mathematica : cpu = 0.241464 (sec), leaf count = 205

DSolve[Derivative[1][y][x] == F[-Log[x] + Log[Log[y[x]]]]*y[x],y[x],x]
 

$$\text{Solve}[{\int }_1^{y(x)}(\frac{1}{K[2](xF(\log (\log (K[2]))-\log (x))-\log (K[2]))}-{\int }_1^x(\frac{F(\log (\log (K[2]))-\log (K[1]))(\frac{K[1]F^{\prime }(\log (\log (K[2]))-\log (K[1]))}{K[2]\log (K[2])}-\frac{1}{K[2]})}{(F(\log (\log (K[2]))-\log (K[1]))K[1]-\log (K[2]){)}^2}-\frac{F^{\prime }(\log (\log (K[2]))-\log (K[1]))}{K[2](F(\log (\log (K[2]))-\log (K[1]))K[1]-\log (K[2]))\log (K[2])})dK[1])dK[2]+{\int }_1^x-\frac{F(\log (\log (y(x)))-\log (K[1]))}{F(\log (\log (y(x)))-\log (K[1]))K[1]-\log (y(x))}dK[1]=c_1,y(x)]$$ ✓ Maple : cpu = 0.491 (sec), leaf count = 120

dsolve(diff(y(x),x) = F(ln(ln(y(x)))-ln(x))*y(x),y(x))
 

$${\int }_{\mathit{\text{\_b}}}^x\frac{F(\ln (\ln \left(y\left(x\right)\right))-\ln \left(\mathit{\text{\_a}}\right))}{\mathit{\text{\_a}}F(\ln (\ln \left(y\left(x\right)\right))-\ln \left(\mathit{\text{\_a}}\right))-\ln \left(y\left(x\right)\right)}d\mathit{\text{\_a}}+{\int }_{}^{y\left(x\right)}(\frac{1}{\mathit{\text{\_f}}(-xF(\ln (\ln \left(\mathit{\text{\_f}}\right))-\ln \left(x\right))+\ln \left(\mathit{\text{\_f}}\right))}-\left({\int }_{\mathit{\text{\_b}}}^x\frac{F(\ln (\ln \left(\mathit{\text{\_f}}\right))-\ln \left(\mathit{\text{\_a}}\right))-D\left(F\right)(\ln (\ln \left(\mathit{\text{\_f}}\right))-\ln \left(\mathit{\text{\_a}}\right))}{{(\mathit{\text{\_a}}F(\ln (\ln \left(\mathit{\text{\_f}}\right))-\ln \left(\mathit{\text{\_a}}\right))-\ln \left(\mathit{\text{\_f}}\right))}^2\mathit{\text{\_f}}}d\mathit{\text{\_a}}\right))d\mathit{\text{\_f}}+c_1=0$$