3.59   ODE No. 59

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

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

Mathematica: cpu = 0.176522 (sec), leaf count = 96 $$\left\{\{y(x)\to \text{InverseFunction}\left[\frac{\frac{b{\tan }^{-1}\left(\frac{\mathrm{\#}\text{1}b}{\sqrt{{\mathrm{\#}\text{1}}^2+1}\sqrt{a^2-b^2}}\right)}{\sqrt{a^2-b^2}}-\frac{b{\tan }^{-1}\left(\frac{\mathrm{\#}\text{1}a}{\sqrt{a^2-b^2}}\right)}{\sqrt{a^2-b^2}}+{\sinh }^{-1}(\mathrm{\#}\text{1})}{a}\mathrm{\&}\right][c_1+x]\}\right\}$$

Maple: cpu = 0.032 (sec), leaf count = 26 $$\{x-{\int }^{y\left(x\right)}{(a\sqrt{{\mathit{\_}\mathit{a}}^2+1}+b)}^{-1}d\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1}=0\}$$

Sage: cpu = 0 (sec), leaf count = 0 $$\text{Maxima was unable to solve this ODE}$$