3.389   ODE No. 389

$$\boxed{{\displaystyle {\left(\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)\right)}^2-(4y\left(x\right)+1)\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+(4y\left(x\right)+1)y\left(x\right)=0}}$$

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

Mathematica: cpu = 0.074009 (sec), leaf count = 109 $$\{\{y(x)\to -\frac{1}{4}{e}^{x-4c_1}(2e^{2c_1}-e^x)\},\{y(x)\to \frac{1}{4}(\sinh (2c_1+x)+\cosh (2c_1+x)-2)(\sinh (2c_1+x)+\cosh (2c_1+x))\},\{y(x)\to \frac{1}{4}(\sinh (2c_1+x)+\cosh (2c_1+x))(\sinh (2c_1+x)+\cosh (2c_1+x)+2)\}\}$$

Maple: cpu = 0.811 (sec), leaf count = 193 $$\{y\left(x\right)=-\frac{1}{4},y\left(x\right)=-\frac{{\left({\mathrm{e}}^x\right)}^2}{2\mathit{\_}\mathit{C}\mathit{1}}(-\frac{\mathit{\_}\mathit{C}\mathit{1}}{{\left({\mathrm{e}}^x\right)}^2}(\sqrt{-\frac{\mathit{\_}\mathit{C}\mathit{1}}{{\left({\mathrm{e}}^x\right)}^2}}-2)\frac{1}{\sqrt{-\frac{\mathit{\_}\mathit{C}\mathit{1}}{{\left({\mathrm{e}}^x\right)}^2}}}+\frac{\mathit{\_}\mathit{C}\mathit{1}}{{\left({\mathrm{e}}^x\right)}^2}+2),y\left(x\right)=\frac{{\left({\mathrm{e}}^x\right)}^2}{2\mathit{\_}\mathit{C}\mathit{1}}(\frac{\mathit{\_}\mathit{C}\mathit{1}}{{\left({\mathrm{e}}^x\right)}^2}(\sqrt{-\frac{\mathit{\_}\mathit{C}\mathit{1}}{{\left({\mathrm{e}}^x\right)}^2}}-2)\frac{1}{\sqrt{-\frac{\mathit{\_}\mathit{C}\mathit{1}}{{\left({\mathrm{e}}^x\right)}^2}}}-\frac{\mathit{\_}\mathit{C}\mathit{1}}{{\left({\mathrm{e}}^x\right)}^2}-2),y\left(x\right)=-\frac{{\left({\mathrm{e}}^x\right)}^2}{2\mathit{\_}\mathit{C}\mathit{1}}(-\frac{\mathit{\_}\mathit{C}\mathit{1}}{{\left({\mathrm{e}}^x\right)}^2}(\sqrt{-\frac{\mathit{\_}\mathit{C}\mathit{1}}{{\left({\mathrm{e}}^x\right)}^2}}+2)\frac{1}{\sqrt{-\frac{\mathit{\_}\mathit{C}\mathit{1}}{{\left({\mathrm{e}}^x\right)}^2}}}+\frac{\mathit{\_}\mathit{C}\mathit{1}}{{\left({\mathrm{e}}^x\right)}^2}+2),y\left(x\right)=\frac{{\left({\mathrm{e}}^x\right)}^2}{2\mathit{\_}\mathit{C}\mathit{1}}(\frac{\mathit{\_}\mathit{C}\mathit{1}}{{\left({\mathrm{e}}^x\right)}^2}(\sqrt{-\frac{\mathit{\_}\mathit{C}\mathit{1}}{{\left({\mathrm{e}}^x\right)}^2}}+2)\frac{1}{\sqrt{-\frac{\mathit{\_}\mathit{C}\mathit{1}}{{\left({\mathrm{e}}^x\right)}^2}}}-\frac{\mathit{\_}\mathit{C}\mathit{1}}{{\left({\mathrm{e}}^x\right)}^2}-2)\}$$