\[ \left (x^2-1\right ) y'(x)^2-y(x)^2+1=0 \] ✓ Mathematica : cpu = 0.0999598 (sec), leaf count = 349
\[\left \{\left \{y(x)\to -\frac {1}{2} e^{-c_1} \sqrt {2 e^{4 c_1} x^2+2 e^{4 c_1} \sqrt {(x-1) (x+1)} x+2 e^{2 c_1}-e^{4 c_1}+2 x^2-2 \sqrt {(x-1) (x+1)} x-1}\right \},\left \{y(x)\to \frac {1}{2} e^{-c_1} \sqrt {2 e^{4 c_1} x^2+2 e^{4 c_1} \sqrt {(x-1) (x+1)} x+2 e^{2 c_1}-e^{4 c_1}+2 x^2-2 \sqrt {(x-1) (x+1)} x-1}\right \},\left \{y(x)\to -\frac {1}{2} \sqrt {2 e^{-2 c_1} x^2+2 e^{2 c_1} x^2+2 e^{-2 c_1} \sqrt {x^2-1} x-2 e^{2 c_1} \sqrt {x^2-1} x-e^{-2 c_1}-e^{2 c_1}+2}\right \},\left \{y(x)\to \frac {1}{2} \sqrt {2 e^{-2 c_1} x^2+2 e^{2 c_1} x^2+2 e^{-2 c_1} \sqrt {x^2-1} x-2 e^{2 c_1} \sqrt {x^2-1} x-e^{-2 c_1}-e^{2 c_1}+2}\right \}\right \}\] ✓ Maple : cpu = 494.224 (sec), leaf count = 166
\[ \left \{ {1\sqrt { \left ( -1+y \left ( x \right ) \right ) \left ( 1+y \left ( x \right ) \right ) }\ln \left ( y \left ( x \right ) +\sqrt { \left ( y \left ( x \right ) \right ) ^{2}-1} \right ) {\frac {1}{\sqrt {-1+y \left ( x \right ) }}}{\frac {1}{\sqrt {1+y \left ( x \right ) }}}}+\int ^{x}\!{\frac {1}{{{\it \_a}}^{2}-1}\sqrt { \left ( {{\it \_a}}^{2}-1 \right ) \left ( \left ( y \left ( x \right ) \right ) ^{2}-1 \right ) }{\frac {1}{\sqrt {-1+y \left ( x \right ) }}}{\frac {1}{\sqrt {1+y \left ( x \right ) }}}}{d{\it \_a}}+{\it \_C1}=0,{1\sqrt { \left ( -1+y \left ( x \right ) \right ) \left ( 1+y \left ( x \right ) \right ) }\ln \left ( y \left ( x \right ) +\sqrt { \left ( y \left ( x \right ) \right ) ^{2}-1} \right ) {\frac {1}{\sqrt {-1+y \left ( x \right ) }}}{\frac {1}{\sqrt {1+y \left ( x \right ) }}}}+\int ^{x}\!-{\frac {1}{{{\it \_a}}^{2}-1}\sqrt { \left ( {{\it \_a}}^{2}-1 \right ) \left ( \left ( y \left ( x \right ) \right ) ^{2}-1 \right ) }{\frac {1}{\sqrt {-1+y \left ( x \right ) }}}{\frac {1}{\sqrt {1+y \left ( x \right ) }}}}{d{\it \_a}}+{\it \_C1}=0,y \left ( x \right ) =-1,y \left ( x \right ) =1 \right \} \]