\[ \boxed { \left ( {x}^{2}-1 \right ) \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}- \left ( y \left ( x \right ) \right ) ^{2}+1=0} \]
Mathematica: cpu = 0.091512 (sec), leaf count = 109 \[ \left \{\left \{y(x)\to \frac {1}{2} \left (e^{-c_1} \sqrt {x^2-1}-e^{c_1} \sqrt {x^2-1}+e^{-c_1} x+e^{c_1} x\right )\right \},\left \{y(x)\to \frac {1}{2} \left (-e^{-c_1} \sqrt {x^2-1}+e^{c_1} \sqrt {x^2-1}+e^{-c_1} x+e^{c_1} x\right )\right \}\right \} \]
Maple: cpu = 10.858 (sec), leaf count = 166 \[ \left \{ {1\sqrt { \left ( -1+y \left ( x \right ) \right ) \left ( 1+y \left ( x \right ) \right ) }\ln \left ( y \left ( x \right ) +\sqrt { \left ( y \left ( x \right ) \right ) ^{2}-1} \right ) {\frac {1}{\sqrt { -1+y \left ( x \right ) }}}{\frac {1}{\sqrt {1+y \left ( x \right ) }}}}+ \int ^{x}\!{\frac {1}{{{\it \_a}}^{2}-1}\sqrt { \left ( {{\it \_a}}^{2} -1 \right ) \left ( \left ( y \left ( x \right ) \right ) ^{2}-1 \right ) }{\frac {1}{\sqrt {-1+y \left ( x \right ) }}}{\frac {1}{\sqrt {1+y \left ( x \right ) }}}}{d{\it \_a}}+{\it \_C1}=0,{1\sqrt { \left ( -1+y \left ( x \right ) \right ) \left ( 1+y \left ( x \right ) \right ) }\ln \left ( y \left ( x \right ) +\sqrt { \left ( y \left ( x \right ) \right ) ^{2}-1} \right ) {\frac {1}{\sqrt {-1+y \left ( x \right ) }}}{ \frac {1}{\sqrt {1+y \left ( x \right ) }}}}+\int ^{x}\!-{\frac {1}{{{ \it \_a}}^{2}-1}\sqrt { \left ( {{\it \_a}}^{2}-1 \right ) \left ( \left ( y \left ( x \right ) \right ) ^{2}-1 \right ) }{\frac {1}{\sqrt { -1+y \left ( x \right ) }}}{\frac {1}{\sqrt {1+y \left ( x \right ) }}}}{d {\it \_a}}+{\it \_C1}=0,y \left ( x \right ) =-1,y \left ( x \right ) =1 \right \} \]