3.803   ODE No. 803

$$\boxed{{\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)=\frac{\mathit{\_}\mathit{F}\mathit{1}({\left(y\left(x\right)\right)}^2-2\ln \left(x\right))}{\sqrt{{\left(y\left(x\right)\right)}^2}x}=0}}$$

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

Mathematica: cpu = 0.080010 (sec), leaf count = 386 $$\text{Solve}[{\int }_1^{y(x)}(-{\int }_1^x(\frac{4K[2]\left(\mathrm{\_}\text{F1}(K[2{]}^2-2\log (K[1]))\right){}^3{\mathrm{\_}\text{F1}}^{\prime }(K[2{]}^2-2\log (K[1]))}{K[1](\left(\mathrm{\_}\text{F1}(K[2{]}^2-2\log (K[1]))\right){}^2-1){}^2}+\frac{4\sqrt{K[2{]}^2}\left(\mathrm{\_}\text{F1}(K[2{]}^2-2\log (K[1]))\right){}^2{\mathrm{\_}\text{F1}}^{\prime }(K[2{]}^2-2\log (K[1]))}{K[1](\left(\mathrm{\_}\text{F1}(K[2{]}^2-2\log (K[1]))\right){}^2-1){}^2}-\frac{4K[2]\mathrm{\_}\text{F1}(K[2{]}^2-2\log (K[1])){\mathrm{\_}\text{F1}}^{\prime }(K[2{]}^2-2\log (K[1]))}{K[1](\left(\mathrm{\_}\text{F1}(K[2{]}^2-2\log (K[1]))\right){}^2-1)}-\frac{2\sqrt{K[2{]}^2}{\mathrm{\_}\text{F1}}^{\prime }(K[2{]}^2-2\log (K[1]))}{K[1](\left(\mathrm{\_}\text{F1}(K[2{]}^2-2\log (K[1]))\right){}^2-1)})dK[1]+\frac{K[2]}{\left(\mathrm{\_}\text{F1}(K[2{]}^2-2\log (x))\right){}^2-1}+\frac{\sqrt{K[2{]}^2}\mathrm{\_}\text{F1}(K[2{]}^2-2\log (x))}{\left(\mathrm{\_}\text{F1}(K[2{]}^2-2\log (x))\right){}^2-1})dK[2]+{\int }_1^x(-\frac{\left(\mathrm{\_}\text{F1}(y(x{)}^2-2\log (K[1]))\right){}^2}{K[1](\left(\mathrm{\_}\text{F1}(y(x{)}^2-2\log (K[1]))\right){}^2-1)}-\frac{\sqrt{y(x{)}^2}\mathrm{\_}\text{F1}(y(x{)}^2-2\log (K[1]))}{y(x)K[1](\left(\mathrm{\_}\text{F1}(y(x{)}^2-2\log (K[1]))\right){}^2-1)})dK[1]=c_1,y(x)]$$

Maple: cpu = 0.327 (sec), leaf count = 65 $$\{y\left(x\right)=\sqrt{2\ln \left(x\right)+2\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(\ln \left(x\right)-{\int }^{\mathit{\_}\mathit{Z}}{(\mathit{\_}\mathit{F}\mathit{1}\left(2\mathit{\_}\mathit{a}\right)-1)}^{-1}d\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1})},y\left(x\right)=-\sqrt{2\ln \left(x\right)+2\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(\ln \left(x\right)-{\int }^{\mathit{\_}\mathit{Z}}{(\mathit{\_}\mathit{F}\mathit{1}\left(2\mathit{\_}\mathit{a}\right)-1)}^{-1}d\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1})}\}$$