2.59   ODE No. 59

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

$$a(-\sqrt{y(x{)}^2+1})-b+y^{\prime }(x)=0$$ ✓ Mathematica : cpu = 0.180019 (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 = 0.052 (sec), leaf count = 26

$$\{x-{\int }^{y\left(x\right)}{(a\sqrt{{\mathit{\_}\mathit{a}}^2+1}+b)}^{-1}d\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1}=0\}$$