\[ \boxed { x \left ( {x}^{2}-1 \right ) {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +y \left ( x \right ) a{x}^{3}=0} \]
Mathematica: cpu = 0.027503 (sec), leaf count = 44 \[ \left \{\left \{y(x)\to c_2 \sin \left (\sqrt {a} \sqrt {x^2-1}\right )+c_1 \cos \left (\sqrt {a} \sqrt {x^2-1}\right )\right \}\right \} \]
Maple: cpu = 0.015 (sec), leaf count = 45 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,\sin \left ( { \left ( 1+x \right ) \left ( x-1 \right ) \sqrt {a}{\frac {1}{\sqrt {{x}^{2}-1}}}} \right ) +{\it \_C2}\,\cos \left ( { \left ( 1+x \right ) \left ( x-1 \right ) \sqrt {a}{\frac {1}{\sqrt {{x}^{2}-1}}}} \right ) \right \} \]