2.447   ODE No. 447

\[ \left (x^2-1\right ) y'(x)^2-1=0 \]

✓ Mathematica : cpu = 0.0074335 (sec), leaf count = 41

DSolve[-1 + (-1 + x^2)*Derivative[1][y][x]^2 == 0,y[x],x]
 

\[\left \{\left \{y(x)\to -\tanh ^{-1}\left (\frac {x}{\sqrt {x^2-1}}\right )+c_1\right \},\left \{y(x)\to \tanh ^{-1}\left (\frac {x}{\sqrt {x^2-1}}\right )+c_1\right \}\right \}\]

✓ Maple : cpu = 0.049 (sec), leaf count = 33

dsolve((x^2-1)*diff(y(x),x)^2-1 = 0,y(x))
 

\[y \left (x \right ) = \ln \left (x +\sqrt {x^{2}-1}\right )+c_{1}\]