\[ \sqrt {x^2-1} y'(x)-\sqrt {y(x)^2-1}=0 \] ✓ Mathematica : cpu = 0.0575981 (sec), leaf count = 143
\[\left \{\left \{y(x)\to -\frac {1}{2} e^{-c_1} \sqrt {e^{4 c_1} \left (2 x^2+2 \sqrt {x^2-1} x-1\right )+2 e^{2 c_1}+2 x^2-2 \sqrt {x^2-1} x-1}\right \},\left \{y(x)\to \frac {1}{2} e^{-c_1} \sqrt {e^{4 c_1} \left (2 x^2+2 \sqrt {x^2-1} x-1\right )+2 e^{2 c_1}+2 x^2-2 \sqrt {x^2-1} x-1}\right \}\right \}\]
✓ Maple : cpu = 0.009 (sec), leaf count = 29
\[ \left \{ \ln \left ( x+\sqrt {{x}^{2}-1} \right ) -\ln \left ( y \left ( x \right ) +\sqrt { \left ( y \left ( x \right ) \right ) ^{2}-1} \right ) +{\it \_C1}=0 \right \} \]