2.923   ODE No. 923

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

$$y^{\prime }(x)=\frac{x^2+2xy(x)+e^{-2(x-y(x))(y(x)+x)}+y(x{)}^2}{x^2+2xy(x)-e^{-2(x-y(x))(y(x)+x)}+y(x{)}^2}$$ ✓ Mathematica : cpu = 1.37901 (sec), leaf count = 432

$$\text{Solve}[{\int }_1^{y(x)}(-\frac{2e^{2(x-K[2])(x+K[2])}K[2]}{-e^{2(x-K[2])(x+K[2])}{x}^2+e^{2(x-K[2])(x+K[2])}K[2{]}^2+1}-{\int }_1^x(-\frac{2e^{2(K[1]-K[2])(K[1]+K[2])}K[1](2(K[1]-K[2])-2(K[1]+K[2]))}{e^{2(K[1]-K[2])(K[1]+K[2])}K[1{]}^2-e^{2(K[1]-K[2])(K[1]+K[2])}K[2{]}^2-1}+\frac{2e^{2(K[1]-K[2])(K[1]+K[2])}K[1](e^{2(K[1]-K[2])(K[1]+K[2])}(2(K[1]-K[2])-2(K[1]+K[2]))K[1{]}^2-2e^{2(K[1]-K[2])(K[1]+K[2])}K[2]-e^{2(K[1]-K[2])(K[1]+K[2])}K[2{]}^2(2(K[1]-K[2])-2(K[1]+K[2])))}{{(e^{2(K[1]-K[2])(K[1]+K[2])}K[1{]}^2-e^{2(K[1]-K[2])(K[1]+K[2])}K[2{]}^2-1)}^2}-\frac{1}{(K[1]+K[2]{)}^2})dK[1]+\frac{1}{x+K[2]})dK[2]+{\int }_1^x(\frac{1}{K[1]+y(x)}-\frac{2e^{2(K[1]-y(x))(K[1]+y(x))}K[1]}{e^{2(K[1]-y(x))(K[1]+y(x))}K[1{]}^2-e^{2(K[1]-y(x))(K[1]+y(x))}y(x{)}^2-1})dK[1]=c_1,y(x)]$$ ✓ Maple : cpu = 0.552 (sec), leaf count = 36

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