\[ \left (a^2 x^2-1\right ) y''(x)+2 a^2 x y'(x)=0 \] ✓ Mathematica : cpu = 0.0148716 (sec), leaf count = 19
\[\left \{\left \{y(x)\to c_2-\frac {c_1 \tanh ^{-1}(a x)}{a}\right \}\right \}\]
✓ Maple : cpu = 0.019 (sec), leaf count = 27
\[ \left \{ y \left ( x \right ) ={\it \_C1}-{\frac { \left ( -\ln \left ( ax-1 \right ) +\ln \left ( ax+1 \right ) \right ) {\it \_C2}}{2\,a}} \right \} \]