2.803   ODE No. 803

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

$$y^{\prime }(x)=\frac{\mathrm{\_}\text{F1}(y(x{)}^2-2\log (x))}{x\sqrt{y(x{)}^2}}$$ ✓ Mathematica : cpu = 0.0875959 (sec), leaf count = 634

$$\text{Solve}[{\int }_1^{y(x)}(-{\int }_1^x(\frac{2K[2]\left(\mathrm{\_}\text{F1}(K[2{]}^2-2\log (K[1]))\right){}^2{\mathrm{\_}\text{F1}}^{\prime }(K[2{]}^2-2\log (K[1]))}{K[1](\mathrm{\_}\text{F1}(K[2{]}^2-2\log (K[1]))-1){}^2(\mathrm{\_}\text{F1}(K[2{]}^2-2\log (K[1]))+1)}+\frac{2K[2]\left(\mathrm{\_}\text{F1}(K[2{]}^2-2\log (K[1]))\right){}^2{\mathrm{\_}\text{F1}}^{\prime }(K[2{]}^2-2\log (K[1]))}{K[1](\mathrm{\_}\text{F1}(K[2{]}^2-2\log (K[1]))-1)(\mathrm{\_}\text{F1}(K[2{]}^2-2\log (K[1]))+1){}^2}-\frac{4K[2]\mathrm{\_}\text{F1}(K[2{]}^2-2\log (K[1])){\mathrm{\_}\text{F1}}^{\prime }(K[2{]}^2-2\log (K[1]))}{K[1](\mathrm{\_}\text{F1}(K[2{]}^2-2\log (K[1]))-1)(\mathrm{\_}\text{F1}(K[2{]}^2-2\log (K[1]))+1)}+\frac{2\sqrt{K[2{]}^2}\mathrm{\_}\text{F1}(K[2{]}^2-2\log (K[1])){\mathrm{\_}\text{F1}}^{\prime }(K[2{]}^2-2\log (K[1]))}{K[1](\mathrm{\_}\text{F1}(K[2{]}^2-2\log (K[1]))-1){}^2(\mathrm{\_}\text{F1}(K[2{]}^2-2\log (K[1]))+1)}+\frac{2\sqrt{K[2{]}^2}\mathrm{\_}\text{F1}(K[2{]}^2-2\log (K[1])){\mathrm{\_}\text{F1}}^{\prime }(K[2{]}^2-2\log (K[1]))}{K[1](\mathrm{\_}\text{F1}(K[2{]}^2-2\log (K[1]))-1)(\mathrm{\_}\text{F1}(K[2{]}^2-2\log (K[1]))+1){}^2}-\frac{2\sqrt{K[2{]}^2}{\mathrm{\_}\text{F1}}^{\prime }(K[2{]}^2-2\log (K[1]))}{K[1](\mathrm{\_}\text{F1}(K[2{]}^2-2\log (K[1]))-1)(\mathrm{\_}\text{F1}(K[2{]}^2-2\log (K[1]))+1)})dK[1]+\frac{\sqrt{K[2{]}^2}\mathrm{\_}\text{F1}(K[2{]}^2-2\log (x))}{(\mathrm{\_}\text{F1}(K[2{]}^2-2\log (x))-1)(\mathrm{\_}\text{F1}(K[2{]}^2-2\log (x))+1)}+\frac{K[2]}{(\mathrm{\_}\text{F1}(K[2{]}^2-2\log (x))-1)(\mathrm{\_}\text{F1}(K[2{]}^2-2\log (x))+1)})dK[2]+{\int }_1^x(-\frac{\left(\mathrm{\_}\text{F1}(y(x{)}^2-2\log (K[1]))\right){}^2}{K[1](\mathrm{\_}\text{F1}(y(x{)}^2-2\log (K[1]))-1)(\mathrm{\_}\text{F1}(y(x{)}^2-2\log (K[1]))+1)}-\frac{\sqrt{y(x{)}^2}\mathrm{\_}\text{F1}(y(x{)}^2-2\log (K[1]))}{y(x)K[1](\mathrm{\_}\text{F1}(y(x{)}^2-2\log (K[1]))-1)(\mathrm{\_}\text{F1}(y(x{)}^2-2\log (K[1]))+1)})dK[1]=c_1,y(x)]$$

✓ Maple : cpu = 0.431 (sec), leaf count = 65

$$\{y\left(x\right)=\sqrt{2\ln \left(x\right)+2\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(\ln \left(x\right)-{\int }^{\mathit{\_}\mathit{Z}}{(\mathit{\_}\mathit{F}\mathit{1}\left(2\mathit{\_}\mathit{a}\right)-1)}^{-1}d\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1})},y\left(x\right)=-\sqrt{2\ln \left(x\right)+2\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(\ln \left(x\right)-{\int }^{\mathit{\_}\mathit{Z}}{(\mathit{\_}\mathit{F}\mathit{1}\left(2\mathit{\_}\mathit{a}\right)-1)}^{-1}d\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1})}\}$$