8.60   ODE No. 1650

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

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

Mathematica: cpu = 0.023503 (sec), leaf count = 30 $$\left\{\{y(x)\to \frac{\sinh \left(c_1\right)\sinh (ax)}{a}+\frac{\cosh \left(c_1\right)\cosh (ax)}{a}+c_2\}\right\}$$

Maple: cpu = 0.125 (sec), leaf count = 18 $$\{y\left(x\right)=\frac{\cosh (\mathit{\_}\mathit{C}\mathit{1}a+ax)}{a}+\mathit{\_}\mathit{C}\mathit{2}\}$$