\[ \boxed { {x}^{2}{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) + \left ( 2\,{x}^{2}\cot \left ( x \right ) +x \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) + \left ( x\cot \left ( x \right ) +a \right ) y \left ( x \right ) =0} \]
Mathematica: cpu = 0.143518 (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 = 0.031 (sec), leaf count = 33 \[ \left \{ y \left ( x \right ) ={\frac {{\it \_C1}}{\sin \left ( x \right ) }{{\sl J}_{i\sqrt {a}}\left (x\right )}}+{\frac {{\it \_C2}}{ \sin \left ( x \right ) }{{\sl Y}_{i\sqrt {a}}\left (x\right )}} \right \} \]