2.190   ODE No. 190

\[ \sqrt {x^2-1} y'(x)-\sqrt {y(x)^2-1}=0 \]

✓ Mathematica : cpu = 0.0905812 (sec), leaf count = 92

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

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

✓ Maple : cpu = 0.01 (sec), leaf count = 29

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

\[\ln \left (x +\sqrt {x^{2}-1}\right )-\ln \left (y \left (x \right )+\sqrt {y \left (x \right )^{2}-1}\right )+c_{1} = 0\]