\[ \boxed { \sqrt { \left ( y \left ( x \right ) \right ) ^{2}-1}{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -\sqrt {{x}^{2}-1}=0} \]
Mathematica: cpu = 0.181023 (sec), leaf count = 75 \[ \left \{\left \{y(x)\to \text {InverseFunction}\left [\frac {1}{2} \text {$\#$1} \sqrt {\text {$\#$1}^2-1}-\frac {1}{2} \log \left (\sqrt {\text {$\#$1}^2-1}+\text {$\#$1}\right )\& \right ]\left [c_1+\frac {1}{2} \sqrt {x^2-1} x-\frac {1}{2} \log \left (\sqrt {x^2-1}+x\right )\right ]\right \}\right \} \]
Maple: cpu = 0.0 (sec), leaf count = 50 \[ \left \{ {\it \_C1}+x\sqrt {{x}^{2}-1}-\ln \left ( x+\sqrt {{x}^{2}-1} \right ) -y \left ( x \right ) \sqrt { \left ( y \left ( x \right ) \right ) ^{2}-1}+\ln \left ( y \left ( x \right ) +\sqrt { \left ( y \left ( x \right ) \right ) ^{2}-1} \right ) =0 \right \} \]