8.110   ODE No. 1700

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

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

Mathematica: cpu = 0.073009 (sec), leaf count = 44 $$\{\{y(x)\to -e^{-c_1}\sinh \left(e^{c_1}(c_2+x)\right)\},\{y(x)\to e^{-c_1}\sinh \left(e^{c_1}(c_2+x)\right)\}\}$$

Maple: cpu = 1.669 (sec), leaf count = 79 $$\{y\left(x\right)=\frac{\mathit{\_}\mathit{C}\mathit{1}}{2}(1{\left({\mathrm{e}}^{\frac{\mathit{\_}\mathit{C}\mathit{2}}{\mathit{\_}\mathit{C}\mathit{1}}}\right)}^{-2}{\left({\mathrm{e}}^{\frac{x}{\mathit{\_}\mathit{C}\mathit{1}}}\right)}^{-2}-1){\mathrm{e}}^{\frac{\mathit{\_}\mathit{C}\mathit{2}}{\mathit{\_}\mathit{C}\mathit{1}}}{\mathrm{e}}^{\frac{x}{\mathit{\_}\mathit{C}\mathit{1}}},y\left(x\right)=\frac{\mathit{\_}\mathit{C}\mathit{1}}{2}({\left({\mathrm{e}}^{\frac{\mathit{\_}\mathit{C}\mathit{2}}{\mathit{\_}\mathit{C}\mathit{1}}}\right)}^2{\left({\mathrm{e}}^{\frac{x}{\mathit{\_}\mathit{C}\mathit{1}}}\right)}^2-1){\left({\mathrm{e}}^{\frac{\mathit{\_}\mathit{C}\mathit{2}}{\mathit{\_}\mathit{C}\mathit{1}}}\right)}^{-1}{\left({\mathrm{e}}^{\frac{x}{\mathit{\_}\mathit{C}\mathit{1}}}\right)}^{-1}\}$$