3.408   ODE No. 408

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

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

Mathematica: cpu = 0.532068 (sec), leaf count = 166 $$\{\text{Solve}[\frac{(\sqrt{\frac{2y(x)}{x}-1}-1)((\sqrt{\frac{2y(x)}{x}-1}-1)\log (\sqrt{\frac{2y(x)}{x}-1}-1)-1)}{\sqrt{\frac{2y(x)}{x}-1}-\frac{y(x)}{x}}=c_1+\log (x),y(x)],\text{Solve}[\frac{(\sqrt{\frac{2y(x)}{x}-1}+1)((\sqrt{\frac{2y(x)}{x}-1}+1)\log (\sqrt{\frac{2y(x)}{x}-1}+1)+1)}{\frac{y(x)}{x}+\sqrt{\frac{2y(x)}{x}-1}}=c_1-\log (x),y(x)]\}$$

Maple: cpu = 0.514 (sec), leaf count = 73 $$\{y\left(x\right)=(\frac{1}{2}{(\mathit{l}\mathit{a}\mathit{m}\mathit{b}\mathit{e}\mathit{r}\mathit{t}\mathit{W}\left(\frac{1}{\mathit{\_}\mathit{C}\mathit{1}}\sqrt{\mathit{\_}\mathit{C}\mathit{1}x}\right)+1)}^2{\left(\mathit{l}\mathit{a}\mathit{m}\mathit{b}\mathit{e}\mathit{r}\mathit{t}\mathit{W}\left(\frac{1}{\mathit{\_}\mathit{C}\mathit{1}}\sqrt{\mathit{\_}\mathit{C}\mathit{1}x}\right)\right)}^{-2}+\frac{1}{2})x,y\left(x\right)=(\frac{1}{2}{(\mathit{l}\mathit{a}\mathit{m}\mathit{b}\mathit{e}\mathit{r}\mathit{t}\mathit{W}(-\frac{1}{\mathit{\_}\mathit{C}\mathit{1}}\sqrt{\mathit{\_}\mathit{C}\mathit{1}x})+1)}^2{\left(\mathit{l}\mathit{a}\mathit{m}\mathit{b}\mathit{e}\mathit{r}\mathit{t}\mathit{W}(-\frac{1}{\mathit{\_}\mathit{C}\mathit{1}}\sqrt{\mathit{\_}\mathit{C}\mathit{1}x})\right)}^{-2}+\frac{1}{2})x\}$$