\[ \left (a^2 x^2-1\right ) y''(x)+2 a^2 x y'(x)-2 a^2 y(x)=0 \] ✓ Mathematica : cpu = 0.0109633 (sec), leaf count = 41
\[\left \{\left \{y(x)\to a c_1 x+c_2 \left (a x \left (\frac {1}{2} \log (a x+1)-\frac {1}{2} \log (1-a x)\right )-1\right )\right \}\right \}\] ✓ Maple : cpu = 0.088 (sec), leaf count = 31
\[ \left \{ y \left ( x \right ) =-{\frac {{\it \_C2}\,a\ln \left ( ax+1 \right ) x}{2}}+{\frac {{\it \_C2}\,a\ln \left ( ax-1 \right ) x}{2}}+{\it \_C1}\,x+{\it \_C2} \right \} \]