\[ \left (x^2+1\right ) y''(x)+x y'(x)-9 y(x)=0 \] ✓ Mathematica : cpu = 0.0180419 (sec), leaf count = 25
\[\left \{\left \{y(x)\to c_1 \cosh \left (3 \sinh ^{-1}(x)\right )+i c_2 \sinh \left (3 \sinh ^{-1}(x)\right )\right \}\right \}\] ✓ Maple : cpu = 0.033 (sec), leaf count = 39
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,\sin \left ( 3\,\arctan \left ( {\frac {x}{\sqrt {-{x}^{2}-1}}} \right ) \right ) +{\it \_C2}\,\cos \left ( 3\,\arctan \left ( {\frac {x}{\sqrt {-{x}^{2}-1}}} \right ) \right ) \right \} \]