8.135   ODE No. 1725

$$\boxed{{\displaystyle \left(\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)\right)(x-y\left(x\right))-(\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+1)({\left(\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)\right)}^2+1)=0}}$$

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

Mathematica: cpu = 0.327042 (sec), leaf count = 75 $$\{\{y(x)\to -\sqrt{-2c_{2}x+e^{2c_1}-c_2^2-x^2}-c_2\},\{y(x)\to \sqrt{-2c_{2}x+e^{2c_1}-c_2^2-x^2}-c_2\}\}$$

Maple: cpu = 1.997 (sec), leaf count = 105 $$\{y\left(x\right)=x+\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-x+{\int }^{\mathit{\_}\mathit{Z}}({\mathit{\_}\mathit{C}\mathit{1}}^2{\mathit{\_}\mathit{f}}^2-1){(-{\mathit{\_}\mathit{C}\mathit{1}}^2{\mathit{\_}\mathit{f}}^2+\mathit{\_}\mathit{C}\mathit{1}\sqrt{-{\mathit{\_}\mathit{C}\mathit{1}}^2{\mathit{\_}\mathit{f}}^2+2}\mathit{\_}\mathit{f}+2)}^{-1}d\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{2}),y\left(x\right)=x+\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-x+{\int }^{\mathit{\_}\mathit{Z}}-({\mathit{\_}\mathit{C}\mathit{1}}^2{\mathit{\_}\mathit{f}}^2-1){({\mathit{\_}\mathit{C}\mathit{1}}^2{\mathit{\_}\mathit{f}}^2+\mathit{\_}\mathit{C}\mathit{1}\sqrt{-{\mathit{\_}\mathit{C}\mathit{1}}^2{\mathit{\_}\mathit{f}}^2+2}\mathit{\_}\mathit{f}-2)}^{-1}d\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{2})\}$$