\[ y(x) (a+x \cot (x))+x^2 y''(x)+\left (2 x^2 \cot (x)+x\right ) y'(x)=0 \] ✓ Mathematica : cpu = 0.143224 (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 = 0.04 (sec), leaf count = 33
\[ \left \{ y \left ( x \right ) ={\frac {{\it \_C1}}{\sin \left ( x \right ) }{{\sl J}_{i\sqrt {a}}\left (x\right )}}+{\frac {{\it \_C2}}{\sin \left ( x \right ) }{{\sl Y}_{i\sqrt {a}}\left (x\right )}} \right \} \]