\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) =-{\frac {ay \left ( x \right ) }{ \left ( \sin \left ( x \right ) \right ) ^{2}}}=0} \]
Mathematica: cpu = 0.072009 (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 = 0.203 (sec), leaf count = 165 \[ \left \{ y \left ( x \right ) ={{\it \_C1}\sqrt [4]{2\,\cos \left ( 2\,x \right ) +2} {\mbox {$_2$F$_1$}({\frac {1}{4}\sqrt {1-4\,a}}+{\frac {1}{4}},{\frac {1}{4}\sqrt {1-4\,a}}+{\frac {1}{4}};\,{\frac {1}{2}};\,{\frac {\cos \left ( 2\,x \right ) }{2}}+{\frac {1}{2}})} \sqrt {-2\,\cos \left ( 2\,x \right ) +2} \left ( {\frac {\cos \left ( 2\, x \right ) }{2}}-{\frac {1}{2}} \right ) ^{{\frac {1}{4}\sqrt {1-4\,a}}} {\frac {1}{\sqrt {\sin \left ( 2\,x \right ) }}}}+{{\it \_C2} \left ( 2\, \cos \left ( 2\,x \right ) +2 \right ) ^{{\frac {3}{4}}} {\mbox {$_2$F$_1$}({\frac {1}{4}\sqrt {1-4\,a}}+{\frac {3}{4}},{\frac {1}{4}\sqrt {1-4\,a}}+{\frac {3}{4}};\,{\frac {3}{2}};\,{\frac {\cos \left ( 2\,x \right ) }{2}}+{\frac {1}{2}})} \sqrt {-2\,\cos \left ( 2\,x \right ) +2} \left ( {\frac {\cos \left ( 2\, x \right ) }{2}}-{\frac {1}{2}} \right ) ^{{\frac {1}{4}\sqrt {1-4\,a}}} {\frac {1}{\sqrt {\sin \left ( 2\,x \right ) }}}} \right \} \]