2.585   ODE No. 585

1. Problem in Latex
2. Mathematica input
3. Maple input

$$y^{\prime }(x)=y(x)F(\log (\log (y(x)))-\log (x))$$ ✓ Mathematica : cpu = 166.81 (sec), leaf count = 141

$$\text{Solve}[c_1={\int }_1^{y(x)}(\frac{1}{xK[2]F(\log (\log (K[2]))-\log (x))-K[2]\log (K[2])}-{\int }_1^x\frac{F^{\prime }(\log (\log (K[2]))-\log (K[1]))-F(\log (\log (K[2]))-\log (K[1]))}{K[2](\log (K[2])-K[1]F(\log (\log (K[2]))-\log (K[1])){)}^2}dK[1])dK[2]+{\int }_1^x-\frac{F(\log (\log (y(x)))-\log (K[1]))}{K[1]F(\log (\log (y(x)))-\log (K[1]))-\log (y(x))}dK[1],y(x)]$$

✓ Maple : cpu = 0.679 (sec), leaf count = 122

$$\{{\int }_{\mathit{\_}\mathit{b}}^x\frac{F(\ln (\ln \left(y\left(x\right)\right))-\ln \left(\mathit{\_}\mathit{a}\right))}{\mathit{\_}\mathit{a}F(\ln (\ln \left(y\left(x\right)\right))-\ln \left(\mathit{\_}\mathit{a}\right))-\ln \left(y\left(x\right)\right)}\mathrm{d}\mathit{\_}\mathit{a}+{\int }^{y\left(x\right)}-\frac{1}{\mathit{\_}\mathit{f}(xF(\ln (\ln \left(\mathit{\_}\mathit{f}\right))-\ln \left(x\right))-\ln \left(\mathit{\_}\mathit{f}\right))}-{\int }_{\mathit{\_}\mathit{b}}^x\frac{F(\ln (\ln \left(\mathit{\_}\mathit{f}\right))-\ln \left(\mathit{\_}\mathit{a}\right))-\text{D}\left(F\right)(\ln (\ln \left(\mathit{\_}\mathit{f}\right))-\ln \left(\mathit{\_}\mathit{a}\right))}{{(\mathit{\_}\mathit{a}F(\ln (\ln \left(\mathit{\_}\mathit{f}\right))-\ln \left(\mathit{\_}\mathit{a}\right))-\ln \left(\mathit{\_}\mathit{f}\right))}^2\mathit{\_}\mathit{f}}\mathrm{d}\mathit{\_}\mathit{a}d\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{1}=0\}$$