\[ \boxed { \left ( {x}^{2}-1 \right ) {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +2\,x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -a=0} \]
Mathematica: cpu = 0.017502 (sec), leaf count = 36 \[ \left \{\left \{y(x)\to \frac {1}{2} \left (a+c_1\right ) \log (1-x)+\frac {1}{2} \left (a-c_1\right ) \log (x+1)+c_2\right \}\right \} \]
Maple: cpu = 0.015 (sec), leaf count = 34 \[ \left \{ y \left ( x \right ) ={\frac {\ln \left ( x-1 \right ) {\it \_C1 }}{2}}+{\frac {\ln \left ( x-1 \right ) a}{2}}-{\frac {\ln \left ( 1+x \right ) {\it \_C1}}{2}}+{\frac {\ln \left ( 1+x \right ) a}{2}}+{\it \_C2} \right \} \]