2.388   ODE No. 388

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

$$y^{\prime }(x{)}^2-2y(x)y^{\prime }(x)-2x=0$$ ✓ Mathematica : cpu = 0.497327 (sec), leaf count = 53

$$\text{Solve}[\{x=\frac{\text{K}\mathrm{\$}\text{317948}{\sinh }^{-1}(\text{K}\mathrm{\$}\text{317948})}{2\sqrt{{\text{K}\mathrm{\$}\text{317948}}^2+1}}+\frac{c_1\text{K}\mathrm{\$}\text{317948}}{\sqrt{{\text{K}\mathrm{\$}\text{317948}}^2+1}},y(x)=\frac{\text{K}\mathrm{\$}\text{317948}}{2}-\frac{x}{\text{K}\mathrm{\$}\text{317948}}\},\{y(x),\text{K}\mathrm{\$}\text{317948}\}]$$ ✓ Maple : cpu = 0.193 (sec), leaf count = 223

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