3.411   ODE No. 411

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

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

Mathematica: cpu = 0.558571 (sec), leaf count = 181 $$\{\text{Solve}[\frac{(\sqrt{\frac{4y(x)}{x}+1}-1)((\sqrt{\frac{4y(x)}{x}+1}-1)\log (\sqrt{\frac{4y(x)}{x}+1}-1)-1)}{2(-\frac{2y(x)}{x}+\sqrt{\frac{4y(x)}{x}+1}-1)}=c_1+\frac{\log (x)}{2},y(x)],\text{Solve}[\frac{(\sqrt{\frac{4y(x)}{x}+1}+1)((\sqrt{\frac{4y(x)}{x}+1}+1)\log (\sqrt{\frac{4y(x)}{x}+1}+1)+1)}{2(\frac{2y(x)}{x}+\sqrt{\frac{4y(x)}{x}+1}+1)}=c_1-\frac{\log (x)}{2},y(x)]\}$$

Maple: cpu = 0.531 (sec), leaf count = 69 $$\{y\left(x\right)=(\frac{1}{4}{\left(\mathit{l}\mathit{a}\mathit{m}\mathit{b}\mathit{e}\mathit{r}\mathit{t}\mathit{W}(-\frac{1}{2}\frac{1}{\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{x}}})\right)}^{-2}+\frac{1}{2}{\left(\mathit{l}\mathit{a}\mathit{m}\mathit{b}\mathit{e}\mathit{r}\mathit{t}\mathit{W}(-\frac{1}{2}\frac{1}{\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{x}}})\right)}^{-1})x,y\left(x\right)=(\frac{1}{4}{\left(\mathit{l}\mathit{a}\mathit{m}\mathit{b}\mathit{e}\mathit{r}\mathit{t}\mathit{W}\left(\frac{1}{2}\frac{1}{\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{x}}}\right)\right)}^{-2}+\frac{1}{2}{\left(\mathit{l}\mathit{a}\mathit{m}\mathit{b}\mathit{e}\mathit{r}\mathit{t}\mathit{W}\left(\frac{1}{2}\frac{1}{\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{x}}}\right)\right)}^{-1})x\}$$