\[ \left (b^2-a^2\right ) y(x)+2 a \cot (a x) y'(x)+y''(x)=0 \] ✓ Mathematica : cpu = 0.107464 (sec), leaf count = 58
\[\left \{\left \{y(x)\to \frac {1}{2} e^{-\sqrt {-b^2} x} \csc (a x) \left (\frac {c_2 e^{2 \sqrt {-b^2} x}}{\sqrt {-b^2}}+2 c_1\right )\right \}\right \}\]
✓ Maple : cpu = 0.047 (sec), leaf count = 24
\[ \left \{ y \left ( x \right ) ={\frac {{\it \_C2}\,\cos \left ( bx \right ) +{\it \_C1}\,\sin \left ( bx \right ) }{\sin \left ( ax \right ) }} \right \} \]