8.111   ODE No. 1701

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

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

Mathematica: cpu = 0.180523 (sec), leaf count = 97 $$\{\{y(x)\to \frac{1}{2}{e}^{-e^{c_1}x-2c_1-e^{c_1}{c}_2}(e^{2e^{c_1}(c_2+x)}+e^{2c_1})\},\{y(x)\to \frac{1}{2}(e^{-e^{c_1}x-2c_1-e^{c_1}{c}_2}+e^{e^{c_1}x+e^{c_1}{c}_2})\}\}$$

Maple: cpu = 1.654 (sec), leaf count = 79 $$\{y\left(x\right)=\frac{\mathit{\_}\mathit{C}\mathit{1}}{2}(1{\left({\mathrm{e}}^{\frac{\mathit{\_}\mathit{C}\mathit{2}}{\mathit{\_}\mathit{C}\mathit{1}}}\right)}^{-2}{\left({\mathrm{e}}^{\frac{x}{\mathit{\_}\mathit{C}\mathit{1}}}\right)}^{-2}+1){\mathrm{e}}^{\frac{\mathit{\_}\mathit{C}\mathit{2}}{\mathit{\_}\mathit{C}\mathit{1}}}{\mathrm{e}}^{\frac{x}{\mathit{\_}\mathit{C}\mathit{1}}},y\left(x\right)=\frac{\mathit{\_}\mathit{C}\mathit{1}}{2}({\left({\mathrm{e}}^{\frac{\mathit{\_}\mathit{C}\mathit{2}}{\mathit{\_}\mathit{C}\mathit{1}}}\right)}^2{\left({\mathrm{e}}^{\frac{x}{\mathit{\_}\mathit{C}\mathit{1}}}\right)}^2+1){\left({\mathrm{e}}^{\frac{\mathit{\_}\mathit{C}\mathit{2}}{\mathit{\_}\mathit{C}\mathit{1}}}\right)}^{-1}{\left({\mathrm{e}}^{\frac{x}{\mathit{\_}\mathit{C}\mathit{1}}}\right)}^{-1}\}$$