2.408   ODE No. 408

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

$$x{y}^{\prime }(x{)}^2-2y(x)+x=0$$ ✓ Mathematica : cpu = 0.148725 (sec), leaf count = 97

$$\{\text{Solve}[-2(\frac{1}{1-\sqrt{\frac{2y(x)}{x}-1}}+\log (1-\sqrt{\frac{2y(x)}{x}-1}))=\log (x)+c_1,y(x)],\text{Solve}[2(\frac{1}{\sqrt{\frac{2y(x)}{x}-1}+1}+\log (\sqrt{\frac{2y(x)}{x}-1}+1))=-\log (x)+c_1,y(x)]\}$$ ✓ Maple : cpu = 0.117 (sec), leaf count = 73

$$\{y\left(x\right)=(\frac{1}{2}{(\mathit{l}\mathit{a}\mathit{m}\mathit{b}\mathit{e}\mathit{r}\mathit{t}\mathit{W}\left(\frac{1}{\mathit{\_}\mathit{C}\mathit{1}}\sqrt{\mathit{\_}\mathit{C}\mathit{1}x}\right)+1)}^2{\left(\mathit{l}\mathit{a}\mathit{m}\mathit{b}\mathit{e}\mathit{r}\mathit{t}\mathit{W}\left(\frac{1}{\mathit{\_}\mathit{C}\mathit{1}}\sqrt{\mathit{\_}\mathit{C}\mathit{1}x}\right)\right)}^{-2}+\frac{1}{2})x,y\left(x\right)=(\frac{1}{2}{(\mathit{l}\mathit{a}\mathit{m}\mathit{b}\mathit{e}\mathit{r}\mathit{t}\mathit{W}(-\frac{1}{\mathit{\_}\mathit{C}\mathit{1}}\sqrt{\mathit{\_}\mathit{C}\mathit{1}x})+1)}^2{\left(\mathit{l}\mathit{a}\mathit{m}\mathit{b}\mathit{e}\mathit{r}\mathit{t}\mathit{W}(-\frac{1}{\mathit{\_}\mathit{C}\mathit{1}}\sqrt{\mathit{\_}\mathit{C}\mathit{1}x})\right)}^{-2}+\frac{1}{2})x\}$$