2.61   ODE No. 61

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

$$y^{\prime }(x)-\frac{\sqrt{x^2-1}}{\sqrt{y(x{)}^2-1}}=0$$ ✓ Mathematica : cpu = 0.188285 (sec), leaf count = 75

$$\left\{\{y(x)\to \text{InverseFunction}[\frac{1}{2}\mathrm{\#}\text{1}\sqrt{{\mathrm{\#}\text{1}}^2-1}-\frac{1}{2}\log (\sqrt{{\mathrm{\#}\text{1}}^2-1}+\mathrm{\#}\text{1})\mathrm{\&}][c_1+\frac{1}{2}\sqrt{x^2-1}x-\frac{1}{2}\log (\sqrt{x^2-1}+x)]\}\right\}$$

✓ Maple : cpu = 0.015 (sec), leaf count = 50

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