\[ \boxed { \left ( {a}^{2}{x}^{2}-1 \right ) {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +2\,{a}^{2}x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -2\,{a}^{2}y \left ( x \right ) =0} \]
Mathematica: cpu = 0.016002 (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 = 0.046 (sec), leaf count = 32 \[ \left \{ y \left ( x \right ) =x{\it \_C1}+{\it \_C2}\, \left ( {\frac {a \ln \left ( ax-1 \right ) x}{2}}-{\frac {a\ln \left ( ax+1 \right ) x}{2 }}+1 \right ) \right \} \]