\[ y''(x)=-\frac {b \cot (x) y'(x)}{a}-\frac {y(x) \csc ^2(x) \left (c \cos ^2(x)+d \cos (x)+e\right )}{a} \] ✓ Mathematica : cpu = 56.9564 (sec), leaf count = 1596424
DSolve[Derivative[2][y][x] == -(((e + d*Cos[x] + c*Cos[x]^2)*Csc[x]^2*y[x])/a) - (b*Cot[x]*Derivative[1][y][x])/a,y[x],x]
\[ \text {Too large to display} \] ✓ Maple : cpu = 0.561 (sec), leaf count = 517
dsolve(diff(diff(y(x),x),x) = -b/sin(x)*cos(x)/a*diff(y(x),x)-(c*cos(x)^2+d*cos(x)+e)/a/sin(x)^2*y(x),y(x))
\[y \left (x \right ) = \left (\sin ^{-\frac {a +b}{2 a}}\left (x \right )\right ) \left (\frac {\cos \left (x \right )}{2}-\frac {1}{2}\right )^{\frac {2 a +\sqrt {a^{2}+\left (-2 b -4 c -4 d -4 e \right ) a +b^{2}}}{4 a}} \left (\hypergeom \left (\left [\frac {\sqrt {a^{2}+\left (-2 b -4 c -4 d -4 e \right ) a +b^{2}}+2 i \sqrt {4 c a -b^{2}}-\sqrt {a^{2}+\left (-2 b -4 c +4 d -4 e \right ) a +b^{2}}+2 a}{4 a}, -\frac {2 i \sqrt {4 c a -b^{2}}+\sqrt {a^{2}+\left (-2 b -4 c +4 d -4 e \right ) a +b^{2}}-\sqrt {a^{2}+\left (-2 b -4 c -4 d -4 e \right ) a +b^{2}}-2 a}{4 a}\right ], \left [-\frac {-2 a +\sqrt {a^{2}+\left (-2 b -4 c +4 d -4 e \right ) a +b^{2}}}{2 a}\right ], \frac {\cos \left (x \right )}{2}+\frac {1}{2}\right ) \left (2 \cos \left (x \right )+2\right )^{-\frac {-2 a +\sqrt {a^{2}+\left (-2 b -4 c +4 d -4 e \right ) a +b^{2}}}{4 a}} c_{1}+\hypergeom \left (\left [\frac {\sqrt {a^{2}+\left (-2 b -4 c -4 d -4 e \right ) a +b^{2}}-2 i \sqrt {4 c a -b^{2}}+\sqrt {a^{2}+\left (-2 b -4 c +4 d -4 e \right ) a +b^{2}}+2 a}{4 a}, \frac {\sqrt {a^{2}+\left (-2 b -4 c -4 d -4 e \right ) a +b^{2}}+2 i \sqrt {4 c a -b^{2}}+\sqrt {a^{2}+\left (-2 b -4 c +4 d -4 e \right ) a +b^{2}}+2 a}{4 a}\right ], \left [\frac {2 a +\sqrt {a^{2}+\left (-2 b -4 c +4 d -4 e \right ) a +b^{2}}}{2 a}\right ], \frac {\cos \left (x \right )}{2}+\frac {1}{2}\right ) \left (2 \cos \left (x \right )+2\right )^{\frac {2 a +\sqrt {a^{2}+\left (-2 b -4 c +4 d -4 e \right ) a +b^{2}}}{4 a}} c_{2}\right )\]