\[ y(x) (a+x \cot (x))+x^2 y''(x)+\left (2 x^2 \cot (x)+x\right ) y'(x)=0 \] ✓ Mathematica : cpu = 0.107503 (sec), leaf count = 38
\[\left \{\left \{y(x)\to c_1 \csc (x) J_{i \sqrt {a}}(x)+c_2 \csc (x) Y_{i \sqrt {a}}(x)\right \}\right \}\] ✓ Maple : cpu = 0.044 (sec), leaf count = 30
\[y \relax (x ) = \frac {c_{2} \BesselY \left (i \sqrt {a}, x\right )+c_{1} \BesselJ \left (i \sqrt {a}, x\right )}{\sin \relax (x )}\]