\[ y''(x)=-\frac {b \cot (x) y'(x)}{a}-\frac {y(x) \csc ^2(x) \left (c \cos ^2(x)+d \cos (x)+e\right )}{a} \] ✓ Mathematica : cpu = 71.9133 (sec), leaf count = 1596424 \[ \text {Too large to display} \] ✓ Maple : cpu = 0.656 (sec), leaf count = 517
\[\left \{y \left (x \right ) = \left (c_{1} \left (2 \cos \left (x \right )+2\right )^{-\frac {-2 a +\sqrt {a^{2}+b^{2}+\left (-2 b -4 c +4 d -4 e \right ) a}}{4 a}} \hypergeom \left (\left [-\frac {-2 a +2 i \sqrt {4 a c -b^{2}}-\sqrt {a^{2}+b^{2}+\left (-2 b -4 c -4 d -4 e \right ) a}+\sqrt {a^{2}+b^{2}+\left (-2 b -4 c +4 d -4 e \right ) a}}{4 a}, \frac {2 a +\sqrt {a^{2}+b^{2}+\left (-2 b -4 c -4 d -4 e \right ) a}+2 i \sqrt {4 a c -b^{2}}-\sqrt {a^{2}+b^{2}+\left (-2 b -4 c +4 d -4 e \right ) a}}{4 a}\right ], \left [-\frac {-2 a +\sqrt {a^{2}+b^{2}+\left (-2 b -4 c +4 d -4 e \right ) a}}{2 a}\right ], \frac {\cos \left (x \right )}{2}+\frac {1}{2}\right )+c_{2} \left (2 \cos \left (x \right )+2\right )^{\frac {2 a +\sqrt {a^{2}+b^{2}+\left (-2 b -4 c +4 d -4 e \right ) a}}{4 a}} \hypergeom \left (\left [\frac {2 a +\sqrt {a^{2}+b^{2}+\left (-2 b -4 c -4 d -4 e \right ) a}+2 i \sqrt {4 a c -b^{2}}+\sqrt {a^{2}+b^{2}+\left (-2 b -4 c +4 d -4 e \right ) a}}{4 a}, \frac {2 a +\sqrt {a^{2}+b^{2}+\left (-2 b -4 c -4 d -4 e \right ) a}-2 i \sqrt {4 a c -b^{2}}+\sqrt {a^{2}+b^{2}+\left (-2 b -4 c +4 d -4 e \right ) a}}{4 a}\right ], \left [\frac {2 a +\sqrt {a^{2}+b^{2}+\left (-2 b -4 c +4 d -4 e \right ) a}}{2 a}\right ], \frac {\cos \left (x \right )}{2}+\frac {1}{2}\right )\right ) \left (\frac {\cos \left (x \right )}{2}-\frac {1}{2}\right )^{\frac {2 a +\sqrt {a^{2}+b^{2}+\left (-2 b -4 c -4 d -4 e \right ) a}}{4 a}} \left (\sin ^{-\frac {a +b}{2 a}}\left (x \right )\right )\right \}\]