2.595   ODE No. 595

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

$$y^{\prime }(x)=\frac{F\left(\frac{xy(x{)}^2+1}{x}\right)}{x^{2}y(x)}$$ ✓ Mathematica : cpu = 18.836 (sec), leaf count = 201

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

✓ Maple : cpu = 0.143 (sec), leaf count = 72

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