2.389   ODE No. 389

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

$$y^{\prime }(x{)}^2-(4y(x)+1)y^{\prime }(x)+y(x)(4y(x)+1)=0$$ ✓ Mathematica : cpu = 0.0461427 (sec), leaf count = 55

$$\{\{y(x)\to \frac{1}{4}{e}^{x-4c_1}(e^x-2e^{2c_1})\},\{y(x)\to \frac{1}{4}{e}^{2c_1+x}(e^{2c_1+x}-2)\}\}$$

✓ Maple : cpu = 3.801 (sec), leaf count = 71

$$\{y\left(x\right)=-\frac{1}{4},y\left(x\right)=\frac{1}{\mathit{\_}\mathit{C}\mathit{1}}(-{\left({\mathrm{e}}^x\right)}^2\sqrt{-\frac{\mathit{\_}\mathit{C}\mathit{1}}{{\left({\mathrm{e}}^x\right)}^2}}+\mathit{\_}\mathit{C}\mathit{1})\frac{1}{\sqrt{-\frac{\mathit{\_}\mathit{C}\mathit{1}}{{\left({\mathrm{e}}^x\right)}^2}}},y\left(x\right)=-\frac{1}{\mathit{\_}\mathit{C}\mathit{1}}({\left({\mathrm{e}}^x\right)}^2\sqrt{-\frac{\mathit{\_}\mathit{C}\mathit{1}}{{\left({\mathrm{e}}^x\right)}^2}}+\mathit{\_}\mathit{C}\mathit{1})\frac{1}{\sqrt{-\frac{\mathit{\_}\mathit{C}\mathit{1}}{{\left({\mathrm{e}}^x\right)}^2}}}\}$$