2.448   ODE No. 448

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

✓ Mathematica : cpu = 0.110828 (sec), leaf count = 191

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

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

✓ Maple : cpu = 7.718 (sec), leaf count = 166

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

\[y \left (x \right ) = -1\]