\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) =-{\frac { \left ( a \left ( \cos \left ( x \right ) \right ) ^{2}+b \left ( \sin \left ( x \right ) \right ) ^{2}+c \right ) y \left ( x \right ) }{ \left ( \sin \left ( x \right ) \right ) ^{2}}}=0} \]
Mathematica: cpu = 0.392050 (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 = 0.218 (sec), leaf count = 219 \[ \left \{ y \left ( x \right ) ={{\it \_C1}\sqrt [4]{2\,\cos \left ( 2\,x \right ) +2} {\mbox {$_2$F$_1$}({\frac {1}{4}\sqrt {-4\,a+1-4\,c}}+{\frac {1}{2}\sqrt {-a+b}}+{\frac {1}{4}},{\frac {1}{4}\sqrt {-4\,a+1-4\,c}}-{\frac {1}{2}\sqrt {-a+b}}+{\frac {1}{4}};\,{\frac {1}{2}};\,{\frac {\cos \left ( 2\,x \right ) }{2}}+{\frac {1}{2}})} \sqrt {-2\,\cos \left ( 2\,x \right ) +2} \left ( {\frac {\cos \left ( 2\, x \right ) }{2}}-{\frac {1}{2}} \right ) ^{{\frac {1}{4}\sqrt {-4\,a+1-4 \,c}}}{\frac {1}{\sqrt {\sin \left ( 2\,x \right ) }}}}+{{\it \_C2} \left ( 2\,\cos \left ( 2\,x \right ) +2 \right ) ^{{\frac {3}{4}}} {\mbox {$_2$F$_1$}({\frac {1}{4}\sqrt {-4\,a+1-4\,c}}+{\frac {1}{2}\sqrt {-a+b}}+{\frac {3}{4}},{\frac {1}{4}\sqrt {-4\,a+1-4\,c}}-{\frac {1}{2}\sqrt {-a+b}}+{\frac {3}{4}};\,{\frac {3}{2}};\,{\frac {\cos \left ( 2\,x \right ) }{2}}+{\frac {1}{2}})} \sqrt {-2\,\cos \left ( 2\,x \right ) +2} \left ( {\frac {\cos \left ( 2\, x \right ) }{2}}-{\frac {1}{2}} \right ) ^{{\frac {1}{4}\sqrt {-4\,a+1-4 \,c}}}{\frac {1}{\sqrt {\sin \left ( 2\,x \right ) }}}} \right \} \]