2.1725   ODE No. 1725

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

$$(x-y(x))y^{″}(x)-(y^{\prime }(x)+1)(y^{\prime }(x{)}^2+1)=0$$ ✓ Mathematica : cpu = 1.7203 (sec), leaf count = 75

$$\{\{y(x)\to -\sqrt{-x^2-2c_{2}x+e^{2c_1}-c_2{}^2}-c_2\},\{y(x)\to \sqrt{-x^2-2c_{2}x+e^{2c_1}-c_2{}^2}-c_2\}\}$$ ✓ Maple : cpu = 3.479 (sec), leaf count = 105

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