\[ \left (b^2-a^2\right ) y(x)+2 a \cot (a x) y'(x)+y''(x)=0 \] ✓ Mathematica : cpu = 0.0623393 (sec), leaf count = 44
\[\left \{\left \{y(x)\to c_1 e^{-i b x} \csc (a x)-\frac {i c_2 e^{i b x} \csc (a x)}{2 b}\right \}\right \}\] ✓ Maple : cpu = 0.289 (sec), leaf count = 24
\[ \left \{ y \left ( x \right ) ={\frac {{\it \_C2}\,\cos \left ( bx \right ) +{\it \_C1}\,\sin \left ( bx \right ) }{\sin \left ( ax \right ) }} \right \} \]