\[ y''(x)=-\frac {b \cot (x) y'(x)}{a}-\frac {y(x) \csc ^2(x) \left (c \cos ^2(x)+d \cos (x)+e\right )}{a} \] ✓ Mathematica : cpu = 119.334 (sec), leaf count = 1
\[\text {$\$$Aborted}\]
✓ Maple : cpu = 0.732 (sec), leaf count = 517
\[ \left \{ y \left ( x \right ) = \left ( \sin \left ( x \right ) \right ) ^{-{\frac {a+b}{2\,a}}} \left ( {\frac {\cos \left ( x \right ) }{2}}-{\frac {1}{2}} \right ) ^{{\frac {1}{4\,a} \left ( 2\,a+\sqrt {{a}^{2}+ \left ( -2\,b-4\,c-4\,d-4\,e \right ) a+{b}^{2}} \right ) }} \left ( {\mbox {$_2$F$_1$}(-{\frac {1}{4\,a} \left ( 2\,i\sqrt {4\,ca-{b}^{2}}-\sqrt {{a}^{2}+ \left ( -2\,b-4\,c-4\,d-4\,e \right ) a+{b}^{2}}+\sqrt {{a}^{2}+ \left ( -2\,b-4\,c+4\,d-4\,e \right ) a+{b}^{2}}-2\,a \right ) },{\frac {1}{4\,a} \left ( \sqrt {{a}^{2}+ \left ( -2\,b-4\,c-4\,d-4\,e \right ) a+{b}^{2}}+2\,i\sqrt {4\,ca-{b}^{2}}-\sqrt {{a}^{2}+ \left ( -2\,b-4\,c+4\,d-4\,e \right ) a+{b}^{2}}+2\,a \right ) };\,-{\frac {1}{2\,a} \left ( -2\,a+\sqrt {{a}^{2}+ \left ( -2\,b-4\,c+4\,d-4\,e \right ) a+{b}^{2}} \right ) };\,{\frac {\cos \left ( x \right ) }{2}}+{\frac {1}{2}})} \left ( 2\,\cos \left ( x \right ) +2 \right ) ^{-{\frac {1}{4\,a} \left ( -2\,a+\sqrt {{a}^{2}+ \left ( -2\,b-4\,c+4\,d-4\,e \right ) a+{b}^{2}} \right ) }}{\it \_C1}+{\mbox {$_2$F$_1$}({\frac {1}{4\,a} \left ( \sqrt {{a}^{2}+ \left ( -2\,b-4\,c-4\,d-4\,e \right ) a+{b}^{2}}+2\,i\sqrt {4\,ca-{b}^{2}}+\sqrt {{a}^{2}+ \left ( -2\,b-4\,c+4\,d-4\,e \right ) a+{b}^{2}}+2\,a \right ) },{\frac {1}{4\,a} \left ( \sqrt {{a}^{2}+ \left ( -2\,b-4\,c-4\,d-4\,e \right ) a+{b}^{2}}-2\,i\sqrt {4\,ca-{b}^{2}}+\sqrt {{a}^{2}+ \left ( -2\,b-4\,c+4\,d-4\,e \right ) a+{b}^{2}}+2\,a \right ) };\,{\frac {1}{2\,a} \left ( 2\,a+\sqrt {{a}^{2}+ \left ( -2\,b-4\,c+4\,d-4\,e \right ) a+{b}^{2}} \right ) };\,{\frac {\cos \left ( x \right ) }{2}}+{\frac {1}{2}})} \left ( 2\,\cos \left ( x \right ) +2 \right ) ^{{\frac {1}{4\,a} \left ( 2\,a+\sqrt {{a}^{2}+ \left ( -2\,b-4\,c+4\,d-4\,e \right ) a+{b}^{2}} \right ) }}{\it \_C2} \right ) \right \} \]