3.191   ODE No. 191

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

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

Mathematica: cpu = 0.030004 (sec), leaf count = 52 $$\{\{y(x)\to \sqrt{{\tan }^2(c_1+{\sin }^{-1}(x))+1}(-\cot (c_1+{\sin }^{-1}(x)))\},\{y(x)\to \sqrt{{\tan }^2(c_1+{\sin }^{-1}(x))+1}\cot (c_1+{\sin }^{-1}(x))\}\}$$

Maple: cpu = 0.015 (sec), leaf count = 16 $$\{\arcsin \left(x\right)+\arctan \left(\frac{1}{\sqrt{{\left(y\left(x\right)\right)}^2-1}}\right)+\mathit{\_}\mathit{C}\mathit{1}=0\}$$