\[ \boxed { \left ( {x}^{2}-1 \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -xy \left ( x \right ) +a=0} \]
Mathematica: cpu = 0.016502 (sec), leaf count = 21 \[ \left \{\left \{y(x)\to a x+c_1 \sqrt {x^2-1}\right \}\right \} \]
Maple: cpu = 0.015 (sec), leaf count = 20 \[ \left \{ y \left ( x \right ) =\sqrt {1+x}\sqrt {x-1}{\it \_C1}+ax \right \} \]