\[ \sqrt {y(x)^2-1} y'(x)-\sqrt {x^2-1}=0 \] ✓ Mathematica : cpu = 0.149084 (sec), leaf count = 75
\[\left \{\left \{y(x)\to \text {InverseFunction}\left [\frac {1}{2} \text {$\#$1} \sqrt {\text {$\#$1}^2-1}-\frac {1}{2} \log \left (\sqrt {\text {$\#$1}^2-1}+\text {$\#$1}\right )\& \right ]\left [\frac {1}{2} \sqrt {x^2-1} x-\frac {1}{2} \log \left (\sqrt {x^2-1}+x\right )+c_1\right ]\right \}\right \}\] ✓ Maple : cpu = 0.008 (sec), leaf count = 50
\[c_{1}+x \sqrt {x^{2}-1}-\ln \left (x +\sqrt {x^{2}-1}\right )-y \relax (x ) \sqrt {y \relax (x )^{2}-1}+\ln \left (y \relax (x )+\sqrt {y \relax (x )^{2}-1}\right ) = 0\]