2.411   ODE No. 411

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

$$\text{Global}\stackrel{`}{}\text{x}{\text{Global}\stackrel{`}{}\text{y}}^{\prime }(\text{Global}\stackrel{`}{}\text{x}{)}^2+\text{Global}\stackrel{`}{}\text{x}{\text{Global}\stackrel{`}{}\text{y}}^{\prime }(\text{Global}\stackrel{`}{}\text{x})-\text{Global}\stackrel{`}{}\text{y}(\text{Global}\stackrel{`}{}\text{x})=0$$ ✓ Mathematica : cpu = 0.549525 (sec), leaf count = 181

$$\{\text{Solve}[\frac{(\sqrt{\frac{4\text{Global}\stackrel{`}{}\text{y}(\text{Global}\stackrel{`}{}\text{x})}{\text{Global}\stackrel{`}{}\text{x}}+1}-1)((\sqrt{\frac{4\text{Global}\stackrel{`}{}\text{y}(\text{Global}\stackrel{`}{}\text{x})}{\text{Global}\stackrel{`}{}\text{x}}+1}-1)\log (\sqrt{\frac{4\text{Global}\stackrel{`}{}\text{y}(\text{Global}\stackrel{`}{}\text{x})}{\text{Global}\stackrel{`}{}\text{x}}+1}-1)-1)}{2(-\frac{2\text{Global}\stackrel{`}{}\text{y}(\text{Global}\stackrel{`}{}\text{x})}{\text{Global}\stackrel{`}{}\text{x}}+\sqrt{\frac{4\text{Global}\stackrel{`}{}\text{y}(\text{Global}\stackrel{`}{}\text{x})}{\text{Global}\stackrel{`}{}\text{x}}+1}-1)}=c_1+\frac{\log (\text{Global}\stackrel{`}{}\text{x})}{2},\text{Global}\stackrel{`}{}\text{y}(\text{Global}\stackrel{`}{}\text{x})],\text{Solve}[\frac{(\sqrt{\frac{4\text{Global}\stackrel{`}{}\text{y}(\text{Global}\stackrel{`}{}\text{x})}{\text{Global}\stackrel{`}{}\text{x}}+1}+1)((\sqrt{\frac{4\text{Global}\stackrel{`}{}\text{y}(\text{Global}\stackrel{`}{}\text{x})}{\text{Global}\stackrel{`}{}\text{x}}+1}+1)\log (\sqrt{\frac{4\text{Global}\stackrel{`}{}\text{y}(\text{Global}\stackrel{`}{}\text{x})}{\text{Global}\stackrel{`}{}\text{x}}+1}+1)+1)}{2(\frac{2\text{Global}\stackrel{`}{}\text{y}(\text{Global}\stackrel{`}{}\text{x})}{\text{Global}\stackrel{`}{}\text{x}}+\sqrt{\frac{4\text{Global}\stackrel{`}{}\text{y}(\text{Global}\stackrel{`}{}\text{x})}{\text{Global}\stackrel{`}{}\text{x}}+1}+1)}=c_1-\frac{\log (\text{Global}\stackrel{`}{}\text{x})}{2},\text{Global}\stackrel{`}{}\text{y}(\text{Global}\stackrel{`}{}\text{x})]\}$$

✓ Maple : cpu = 0.041 (sec), leaf count = 69

$$\{y\left(x\right)=(\frac{1}{4}{\left(\mathit{l}\mathit{a}\mathit{m}\mathit{b}\mathit{e}\mathit{r}\mathit{t}\mathit{W}(-\frac{1}{2}\frac{1}{\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{x}}})\right)}^{-2}+\frac{1}{2}{\left(\mathit{l}\mathit{a}\mathit{m}\mathit{b}\mathit{e}\mathit{r}\mathit{t}\mathit{W}(-\frac{1}{2}\frac{1}{\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{x}}})\right)}^{-1})x,y\left(x\right)=(\frac{1}{4}{\left(\mathit{l}\mathit{a}\mathit{m}\mathit{b}\mathit{e}\mathit{r}\mathit{t}\mathit{W}\left(\frac{1}{2}\frac{1}{\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{x}}}\right)\right)}^{-2}+\frac{1}{2}{\left(\mathit{l}\mathit{a}\mathit{m}\mathit{b}\mathit{e}\mathit{r}\mathit{t}\mathit{W}\left(\frac{1}{2}\frac{1}{\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{x}}}\right)\right)}^{-1})x\}$$