\[ y''(x)=y(x) \left (-\csc ^2(x)\right ) \left (a \cos ^2(x)+b \sin ^2(x)+c\right ) \] ✓ Mathematica : cpu = 0.335624 (sec), leaf count = 104
\[\left \{\left \{y(x)\to c_1 \sqrt [4]{\cos ^2(x)-1} P_{\frac {1}{2} \left (2 \sqrt {b-a}-1\right )}^{\frac {1}{2} \sqrt {-4 a-4 c+1}}(\cos (x))+c_2 \sqrt [4]{\cos ^2(x)-1} Q_{\frac {1}{2} \left (2 \sqrt {b-a}-1\right )}^{\frac {1}{2} \sqrt {-4 a-4 c+1}}(\cos (x))\right \}\right \}\] ✓ Maple : cpu = 2.491 (sec), leaf count = 183
\[ \left \{ y \left ( x \right ) ={ \left ( {\frac {\cos \left ( 2\,x \right ) }{2}}-{\frac {1}{2}} \right ) ^{{\frac {1}{4}\sqrt {-4\,a+1-4\,c}}}\sqrt [4]{2\,\cos \left ( 2\,x \right ) +2}\sqrt {-2\,\cos \left ( 2\,x \right ) +2} \left ( \sqrt {2\,\cos \left ( 2\,x \right ) +2}{\mbox {$_2$F$_1$}({\frac {1}{4}\sqrt {-4\,a+1-4\,c}}-{\frac {1}{2}\sqrt {-a+b}}+{\frac {3}{4}},{\frac {1}{4}\sqrt {-4\,a+1-4\,c}}+{\frac {1}{2}\sqrt {-a+b}}+{\frac {3}{4}};\,{\frac {3}{2}};\,{\frac {\cos \left ( 2\,x \right ) }{2}}+{\frac {1}{2}})}{\it \_C2}+{\mbox {$_2$F$_1$}({\frac {1}{4}\sqrt {-4\,a+1-4\,c}}+{\frac {1}{2}\sqrt {-a+b}}+{\frac {1}{4}},{\frac {1}{4}\sqrt {-4\,a+1-4\,c}}-{\frac {1}{2}\sqrt {-a+b}}+{\frac {1}{4}};\,{\frac {1}{2}};\,{\frac {\cos \left ( 2\,x \right ) }{2}}+{\frac {1}{2}})}{\it \_C1} \right ) {\frac {1}{\sqrt {\sin \left ( 2\,x \right ) }}}} \right \} \]