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 = 0.0445709 (sec), leaf count = 57

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

✓ Maple : cpu = 0.54 (sec), leaf count = 193

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