\[ \left (x^2-1\right ) y'(x)^2-1=0 \] ✓ Mathematica : cpu = 0.0096007 (sec), leaf count = 89
DSolve[-1 + (-1 + x^2)*Derivative[1][y][x]^2 == 0,y[x],x]
\[\left \{\left \{y(x)\to \frac {1}{2} \log \left (1-\frac {x}{\sqrt {x^2-1}}\right )-\frac {1}{2} \log \left (\frac {x}{\sqrt {x^2-1}}+1\right )+c_1\right \},\left \{y(x)\to -\frac {1}{2} \log \left (1-\frac {x}{\sqrt {x^2-1}}\right )+\frac {1}{2} \log \left (\frac {x}{\sqrt {x^2-1}}+1\right )+c_1\right \}\right \}\] ✓ Maple : cpu = 0.034 (sec), leaf count = 33
dsolve((x^2-1)*diff(y(x),x)^2-1 = 0,y(x))
\[y \left (x \right ) = \ln \left (x +\sqrt {x^{2}-1}\right )+c_{1}\]