3.388   ODE No. 388

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

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

Mathematica: cpu = 0.670085 (sec), leaf count = 53 $$\text{Solve}[\{x=\frac{c_1\text{K}\mathrm{\$}\text{1205645}}{\sqrt{{\text{K}\mathrm{\$}\text{1205645}}^2+1}}+\frac{\text{K}\mathrm{\$}\text{1205645}{\sinh }^{-1}(\text{K}\mathrm{\$}\text{1205645})}{2\sqrt{{\text{K}\mathrm{\$}\text{1205645}}^2+1}},y(x)=\frac{\text{K}\mathrm{\$}\text{1205645}}{2}-\frac{x}{\text{K}\mathrm{\$}\text{1205645}}\},\{y(x),\text{K}\mathrm{\$}\text{1205645}\}]$$

Maple: cpu = 0.499 (sec), leaf count = 217 $$\{\mathit{\_}\mathit{C}\mathit{1}(-2y\left(x\right)+2\sqrt{{\left(y\left(x\right)\right)}^2+2x})\frac{1}{\sqrt{2{\left(y\left(x\right)\right)}^2+2x-2y\left(x\right)\sqrt{{\left(y\left(x\right)\right)}^2+2x}+1}}+x-\frac{1}{2}(-y\left(x\right)+\sqrt{{\left(y\left(x\right)\right)}^2+2x})\mathit{A}\mathit{r}\mathit{c}\mathit{s}\mathit{i}\mathit{n}\mathit{h}(-y\left(x\right)+\sqrt{{\left(y\left(x\right)\right)}^2+2x})\frac{1}{\sqrt{2{\left(y\left(x\right)\right)}^2+2x-2y\left(x\right)\sqrt{{\left(y\left(x\right)\right)}^2+2x}+1}}=0,\mathit{\_}\mathit{C}\mathit{1}(2y\left(x\right)+2\sqrt{{\left(y\left(x\right)\right)}^2+2x})\frac{1}{\sqrt{2{\left(y\left(x\right)\right)}^2+2x+2y\left(x\right)\sqrt{{\left(y\left(x\right)\right)}^2+2x}+1}}+x-\frac{1}{2}(y\left(x\right)+\sqrt{{\left(y\left(x\right)\right)}^2+2x})\mathit{A}\mathit{r}\mathit{c}\mathit{s}\mathit{i}\mathit{n}\mathit{h}(y\left(x\right)+\sqrt{{\left(y\left(x\right)\right)}^2+2x})\frac{1}{\sqrt{2{\left(y\left(x\right)\right)}^2+2x+2y\left(x\right)\sqrt{{\left(y\left(x\right)\right)}^2+2x}+1}}=0\}$$