2.387   ODE No. 387

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

$${\text{Global}\stackrel{`}{}\text{y}}^{\prime }(\text{Global}\stackrel{`}{}\text{x}{)}^2+e^{\text{Global}\stackrel{`}{}\text{x}}({\text{Global}\stackrel{`}{}\text{y}}^{\prime }(\text{Global}\stackrel{`}{}\text{x})-\text{Global}\stackrel{`}{}\text{y}(\text{Global}\stackrel{`}{}\text{x}))=0$$ ✓ Mathematica : cpu = 0.526824 (sec), leaf count = 134

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

✓ Maple : cpu = 0.669 (sec), leaf count = 115

$$\{-\frac{1}{2y\left(x\right)}\sqrt{{\mathrm{e}}^{2x}+4y\left(x\right){\mathrm{e}}^x}-2\mathit{A}\mathit{r}\mathit{t}\mathit{a}\mathit{n}\mathit{h}\left(\sqrt{{\mathrm{e}}^{2x}+4y\left(x\right){\mathrm{e}}^x}{\mathrm{e}}^{-x}\right)-\frac{{\mathrm{e}}^x}{2y\left(x\right)}+\ln \left(y\left(x\right)\right)-\mathit{\_}\mathit{C}\mathit{1}=0,-\frac{{\mathrm{e}}^x}{2y\left(x\right)}+\ln \left(y\left(x\right)\right)+\frac{1}{2y\left(x\right)}\sqrt{{\mathrm{e}}^{2x}+4y\left(x\right){\mathrm{e}}^x}+2\mathit{A}\mathit{r}\mathit{t}\mathit{a}\mathit{n}\mathit{h}\left(\sqrt{{\mathrm{e}}^{2x}+4y\left(x\right){\mathrm{e}}^x}{\mathrm{e}}^{-x}\right)-\mathit{\_}\mathit{C}\mathit{1}=0\}$$