2.374   ODE No. 374

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

$$y^{\prime }(x{)}^2-2y^{\prime }(x)-y(x{)}^2=0$$ ✓ Mathematica : cpu = 0.0649606 (sec), leaf count = 73

$$\{\{y(x)\to \text{InverseFunction}[-\frac{\sqrt{{\mathrm{\#}\text{1}}^2+1}}{\mathrm{\#}\text{1}}-\frac{1}{\mathrm{\#}\text{1}}+{\sinh }^{-1}(\mathrm{\#}\text{1})\mathrm{\&}][c_1-x]\},\{y(x)\to \text{InverseFunction}[-\frac{\sqrt{{\mathrm{\#}\text{1}}^2+1}}{\mathrm{\#}\text{1}}+\frac{1}{\mathrm{\#}\text{1}}+{\sinh }^{-1}(\mathrm{\#}\text{1})\mathrm{\&}][c_1+x]\}\}$$

✓ Maple : cpu = 0.651 (sec), leaf count = 85

$$\{x-{\left(y\left(x\right)\right)}^{-1}-\frac{1}{y\left(x\right)}{({\left(y\left(x\right)\right)}^2+1)}^{\frac{3}{2}}+y\left(x\right)\sqrt{{\left(y\left(x\right)\right)}^2+1}+\mathit{A}\mathit{r}\mathit{c}\mathit{s}\mathit{i}\mathit{n}\mathit{h}\left(y\left(x\right)\right)-\mathit{\_}\mathit{C}\mathit{1}=0,x-{\left(y\left(x\right)\right)}^{-1}+\frac{1}{y\left(x\right)}{({\left(y\left(x\right)\right)}^2+1)}^{\frac{3}{2}}-y\left(x\right)\sqrt{{\left(y\left(x\right)\right)}^2+1}-\mathit{A}\mathit{r}\mathit{c}\mathit{s}\mathit{i}\mathit{n}\mathit{h}\left(y\left(x\right)\right)-\mathit{\_}\mathit{C}\mathit{1}=0\}$$