\[ a x^3 y(x)+\left (x^2-1\right ) x y''(x)+y'(x)=0 \] ✓ Mathematica : cpu = 0.021254 (sec), leaf count = 44
\[\left \{\left \{y(x)\to c_1 \cos \left (\sqrt {a} \sqrt {x^2-1}\right )+c_2 \sin \left (\sqrt {a} \sqrt {x^2-1}\right )\right \}\right \}\] ✓ Maple : cpu = 0.11 (sec), leaf count = 45
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,\sin \left ( { \left ( 1+x \right ) \left ( x-1 \right ) \sqrt {a}{\frac {1}{\sqrt {{x}^{2}-1}}}} \right ) +{\it \_C2}\,\cos \left ( { \left ( 1+x \right ) \left ( x-1 \right ) \sqrt {a}{\frac {1}{\sqrt {{x}^{2}-1}}}} \right ) \right \} \]