\[ y''(x)=y(x) \left (-\csc ^2(x)\right ) \left (a \cos ^2(x)+b \sin ^2(x)+c\right ) \] ✓ Mathematica : cpu = 0.413331 (sec), leaf count = 87
\[\left \{\left \{y(x)\to \sqrt [4]{-\sin ^2(x)} \left (c_1 P_{\sqrt {b-a}-\frac {1}{2}}^{\frac {1}{2} \sqrt {-4 a-4 c+1}}(\cos (x))+c_2 Q_{\sqrt {b-a}-\frac {1}{2}}^{\frac {1}{2} \sqrt {-4 a-4 c+1}}(\cos (x))\right )\right \}\right \}\]
✓ Maple : cpu = 0.522 (sec), leaf count = 183
\[ \left \{ y \left ( x \right ) ={1\sqrt [4]{2\,\cos \left ( 2\,x \right ) +2} \left ( {\frac {\cos \left ( 2\,x \right ) }{2}}-{\frac {1}{2}} \right ) ^{{\frac {1}{4}\sqrt {-4\,a+1-4\,c}}}\sqrt {-2\,\cos \left ( 2\,x \right ) +2} \left ( {\mbox {$_2$F$_1$}({\frac {1}{4}\sqrt {-4\,a+1-4\,c}}+{\frac {1}{2}\sqrt {-a+b}}+{\frac {3}{4}},{\frac {1}{4}\sqrt {-4\,a+1-4\,c}}-{\frac {1}{2}\sqrt {-a+b}}+{\frac {3}{4}};\,{\frac {3}{2}};\,{\frac {\cos \left ( 2\,x \right ) }{2}}+{\frac {1}{2}})}\sqrt {2\,\cos \left ( 2\,x \right ) +2}{\it \_C2}+{\mbox {$_2$F$_1$}({\frac {1}{4}\sqrt {-4\,a+1-4\,c}}+{\frac {1}{2}\sqrt {-a+b}}+{\frac {1}{4}},{\frac {1}{4}\sqrt {-4\,a+1-4\,c}}-{\frac {1}{2}\sqrt {-a+b}}+{\frac {1}{4}};\,{\frac {1}{2}};\,{\frac {\cos \left ( 2\,x \right ) }{2}}+{\frac {1}{2}})}{\it \_C1} \right ) {\frac {1}{\sqrt {\sin \left ( 2\,x \right ) }}}} \right \} \]