\[ \boxed { \left ( -{a}^{2}+{x}^{2} \right ) {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +8\,x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +12\,y \left ( x \right ) =0} \]
Mathematica: cpu = 0.047506 (sec), leaf count = 41 \[ \left \{\left \{y(x)\to \frac {c_2 \left (a^2+3 x^2\right )}{3 (a-x)^3 (a+x)^3}+\frac {c_1}{(a+x)^3}\right \}\right \} \]
Maple: cpu = 0.016 (sec), leaf count = 52 \[ \left \{ y \left ( x \right ) ={\frac {{\it \_C1}\, \left ( {a}^{2}+3\,{x }^{2} \right ) }{ \left ( a-x \right ) ^{3} \left ( x+a \right ) ^{3}}}+{ \frac {{\it \_C2}\,x \left ( 3\,{a}^{2}+{x}^{2} \right ) }{ \left ( a-x \right ) ^{3} \left ( x+a \right ) ^{3}}} \right \} \]