3.387   ODE No. 387

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

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

Mathematica: cpu = 0.535568 (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 = 1.202 (sec), leaf count = 115 $$\{-\frac{{\mathrm{e}}^x}{2y\left(x\right)}+\ln \left(y\left(x\right)\right)+2\mathit{A}\mathit{r}\mathit{t}\mathit{a}\mathit{n}\mathit{h}\left(\sqrt{{\mathrm{e}}^{2x}+4y\left(x\right){\mathrm{e}}^x}{\mathrm{e}}^{-x}\right)+\frac{1}{2y\left(x\right)}\sqrt{{\mathrm{e}}^{2x}+4y\left(x\right){\mathrm{e}}^x}-\mathit{\_}\mathit{C}\mathit{1}=0,-2\mathit{A}\mathit{r}\mathit{t}\mathit{a}\mathit{n}\mathit{h}\left(\sqrt{{\mathrm{e}}^{2x}+4y\left(x\right){\mathrm{e}}^x}{\mathrm{e}}^{-x}\right)-\frac{1}{2y\left(x\right)}\sqrt{{\mathrm{e}}^{2x}+4y\left(x\right){\mathrm{e}}^x}-\frac{{\mathrm{e}}^x}{2y\left(x\right)}+\ln \left(y\left(x\right)\right)-\mathit{\_}\mathit{C}\mathit{1}=0\}$$