\[ \left (b^2-a^2\right ) y(x)+2 a \cot (a x) y'(x)+y''(x)=0 \] ✓ Mathematica : cpu = 0.074339 (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 = 0.077 (sec), leaf count = 24
\[\left \{y \left (x \right ) = \frac {c_{1} \sin \left (b x \right )+c_{2} \cos \left (b x \right )}{\sin \left (a x \right )}\right \}\]