ODE No. 190

$$\sqrt{x^2-1}{y}^{\prime }(x)-\sqrt{y(x{)}^2-1}=0$$ ✓ Mathematica : cpu = 0.0782209 (sec), leaf count = 173

DSolve[-Sqrt[-1 + y[x]^2] + Sqrt[-1 + x^2]*Derivative[1][y][x] == 0,y[x],x]
 

$$\{\{y(x)\to -\frac{1}{2}{e}^{-c_1}\sqrt{2x^2+2e^{4c_1}{x}^2-2\sqrt{(x-1)(x+1)}x+2e^{4c_1}\sqrt{(x-1)(x+1)}x-1+2e^{2c_1}-e^{4c_1}}\},\{y(x)\to \frac{1}{2}{e}^{-c_1}\sqrt{2x^2+2e^{4c_1}{x}^2-2\sqrt{(x-1)(x+1)}x+2e^{4c_1}\sqrt{(x-1)(x+1)}x-1+2e^{2c_1}-e^{4c_1}}\}\}$$ ✓ Maple : cpu = 0.007 (sec), leaf count = 29

dsolve((x^2-1)^(1/2)*diff(y(x),x)-(y(x)^2-1)^(1/2) = 0,y(x))
 

$$\ln (x+\sqrt{x^2-1})-\ln (y\left(x\right)+\sqrt{y{\left(x\right)}^2-1})+c_1=0$$