\[ y''(x)=-a y(x) \csc ^2(x) \] ✓ Mathematica : cpu = 0.0624715 (sec), leaf count = 70
\[\left \{\left \{y(x)\to c_1 \sqrt [4]{\cos ^2(x)-1} P_{-\frac {1}{2}}^{\frac {1}{2} \sqrt {1-4 a}}(\cos (x))+c_2 \sqrt [4]{\cos ^2(x)-1} Q_{-\frac {1}{2}}^{\frac {1}{2} \sqrt {1-4 a}}(\cos (x))\right \}\right \}\] ✓ Maple : cpu = 0.325 (sec), leaf count = 132
\[\left \{y \left (x \right ) = \frac {\left (2 \cos \left (2 x \right )+2\right )^{\frac {1}{4}} \sqrt {-2 \cos \left (2 x \right )+2}\, \left (c_{1} \hypergeom \left (\left [\frac {\sqrt {-4 a +1}}{4}+\frac {1}{4}, \frac {\sqrt {-4 a +1}}{4}+\frac {1}{4}\right ], \left [\frac {1}{2}\right ], \frac {\cos \left (2 x \right )}{2}+\frac {1}{2}\right )+c_{2} \sqrt {2 \cos \left (2 x \right )+2}\, \hypergeom \left (\left [\frac {\sqrt {-4 a +1}}{4}+\frac {3}{4}, \frac {\sqrt {-4 a +1}}{4}+\frac {3}{4}\right ], \left [\frac {3}{2}\right ], \frac {\cos \left (2 x \right )}{2}+\frac {1}{2}\right )\right ) \left (\frac {\cos \left (2 x \right )}{2}-\frac {1}{2}\right )^{\frac {\sqrt {-4 a +1}}{4}}}{\sqrt {\sin \left (2 x \right )}}\right \}\]