\[ \sqrt {\text {Global$\grave { }$y}(\text {Global$\grave { }$x})^2-1} \text {Global$\grave { }$y}'(\text {Global$\grave { }$x})-\sqrt {\text {Global$\grave { }$x}^2-1}=0 \] ✓ Mathematica : cpu = 0.174301 (sec), leaf count = 75
\[\left \{\left \{\text {Global$\grave { }$y}(\text {Global$\grave { }$x})\to \text {InverseFunction}\left [\frac {1}{2} \text {$\#$1} \sqrt {\text {$\#$1}^2-1}-\frac {1}{2} \log \left (\sqrt {\text {$\#$1}^2-1}+\text {$\#$1}\right )\& \right ]\left [c_1+\frac {1}{2} \sqrt {\text {Global$\grave { }$x}^2-1} \text {Global$\grave { }$x}-\frac {1}{2} \log \left (\sqrt {\text {Global$\grave { }$x}^2-1}+\text {Global$\grave { }$x}\right )\right ]\right \}\right \}\]
✓ Maple : cpu = 0.015 (sec), leaf count = 50
\[ \left \{ {\it \_C1}+x\sqrt {{x}^{2}-1}-\ln \left ( x+\sqrt {{x}^{2}-1} \right ) -y \left ( x \right ) \sqrt { \left ( y \left ( x \right ) \right ) ^{2}-1}+\ln \left ( y \left ( x \right ) +\sqrt { \left ( y \left ( x \right ) \right ) ^{2}-1} \right ) =0 \right \} \]