2.387   ODE No. 387

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

$$y^{\prime }(x{)}^2+e^x(y^{\prime }(x)-y(x))=0$$ ✓ Mathematica : cpu = 0.521971 (sec), leaf count = 134

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

✓ Maple : cpu = 0.639 (sec), leaf count = 115

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