3.409   ODE No. 409

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

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

Mathematica: cpu = 30.779909 (sec), leaf count = 66 $$\text{Solve}[\{x=\frac{y(\text{K}\mathrm{\$}\text{1211643})+2\text{K}\mathrm{\$}\text{1211643}}{{\text{K}\mathrm{\$}\text{1211643}}^2},y(x)=c_1{e}^{2(\log (\text{K}\mathrm{\$}\text{1211643})-\log (1-\text{K}\mathrm{\$}\text{1211643}))}+e^{2(\log (\text{K}\mathrm{\$}\text{1211643})-\log (1-\text{K}\mathrm{\$}\text{1211643}))}(-\frac{2}{\text{K}\mathrm{\$}\text{1211643}}-2\log (\text{K}\mathrm{\$}\text{1211643}))\},\{y(x),\text{K}\mathrm{\$}\text{1211643}\}]$$

Maple: cpu = 0.468 (sec), leaf count = 63 $$\{y\left(x\right)=x{\mathrm{e}}^{2\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-x{\mathrm{e}}^{2\mathit{\_}\mathit{Z}}+2x{\mathrm{e}}^{\mathit{\_}\mathit{Z}}+2{\mathrm{e}}^{\mathit{\_}\mathit{Z}}+\mathit{\_}\mathit{C}\mathit{1}-2\mathit{\_}\mathit{Z}-x)}-2{\mathrm{e}}^{\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-x{\mathrm{e}}^{2\mathit{\_}\mathit{Z}}+2x{\mathrm{e}}^{\mathit{\_}\mathit{Z}}+2{\mathrm{e}}^{\mathit{\_}\mathit{Z}}+\mathit{\_}\mathit{C}\mathit{1}-2\mathit{\_}\mathit{Z}-x)}\}$$