2.620   ODE No. 620

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

$$y^{\prime }(x)=\frac{e^{2F(-(x-y(x))(y(x)+x))}+x^2+2xy(x)+y(x{)}^2}{-e^{2F(-(x-y(x))(y(x)+x))}+x^2+2xy(x)+y(x{)}^2}$$ ✓ Mathematica : cpu = 0.762136 (sec), leaf count = 210

$$\text{Solve}[{\int }_1^{y(x)}(-\frac{2K[2]}{-x^2+e^{2F(-(x-K[2])(x+K[2]))}+K[2{]}^2}-{\int }_1^x(\frac{2K[1](-4\exp (2F(-(K[1]-K[2])(K[1]+K[2])))F^{\prime }(-(K[1]-K[2])(K[1]+K[2]))K[2]-2K[2])}{{(K[1{]}^2-\exp (2F(-(K[1]-K[2])(K[1]+K[2])))-K[2{]}^2)}^2}-\frac{1}{(K[1]+K[2]{)}^2})dK[1]+\frac{1}{x+K[2]})dK[2]+{\int }_1^x(\frac{1}{K[1]+y(x)}-\frac{2K[1]}{K[1{]}^2-\exp (2F(-(K[1]-y(x))(K[1]+y(x))))-y(x{)}^2})dK[1]=c_1,y(x)]$$ ✓ Maple : cpu = 0.492 (sec), leaf count = 37

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