2.61   ODE No. 61

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

✓ Mathematica : cpu = 0.146527 (sec), leaf count = 75

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

\[\left \{\left \{y(x)\to \text {InverseFunction}\left [\frac {1}{2} \text {$\#$1} \sqrt {\text {$\#$1}^2-1}-\frac {1}{2} \tanh ^{-1}\left (\frac {\text {$\#$1}}{\sqrt {\text {$\#$1}^2-1}}\right )\& \right ]\left [\frac {1}{2} \sqrt {x^2-1} x-\frac {1}{2} \tanh ^{-1}\left (\frac {x}{\sqrt {x^2-1}}\right )+c_1\right ]\right \}\right \}\]

✓ Maple : cpu = 0.017 (sec), leaf count = 50

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

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