\[ y''(x)=-\frac {b \cot (x) y'(x)}{a}-\frac {y(x) \csc ^2(x) \left (c \cos ^2(x)+d \cos (x)+e\right )}{a} \] ✗ Mathematica : cpu = 203.05 (sec), leaf count = 0
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]
, could not solve
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]
✓ Maple : cpu = 0.827 (sec), leaf count = 513
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))
\[y \left (x \right ) = \sin \left (x \right )^{-\frac {a +b}{2 a}} \left (\frac {\cos \left (x \right )}{2}-\frac {1}{2}\right )^{\frac {2 a +\sqrt {a^{2}+\left (-2 b -4 c -4 d -4 e \right ) a +b^{2}}}{4 a}} \left (\cos \left (\frac {x}{2}\right )^{-\frac {-2 a +\sqrt {a^{2}+\left (-2 b -4 c +4 d -4 e \right ) a +b^{2}}}{2 a}} \operatorname {hypergeom}\left (\left [\frac {\sqrt {a^{2}+\left (-2 b -4 c -4 d -4 e \right ) a +b^{2}}+2 i \sqrt {4 a c -b^{2}}-\sqrt {a^{2}+\left (-2 b -4 c +4 d -4 e \right ) a +b^{2}}+2 a}{4 a}, \frac {\sqrt {a^{2}+\left (-2 b -4 c -4 d -4 e \right ) a +b^{2}}-2 i \sqrt {4 a c -b^{2}}-\sqrt {a^{2}+\left (-2 b -4 c +4 d -4 e \right ) a +b^{2}}+2 a}{4 a}\right ], \left [-\frac {-2 a +\sqrt {a^{2}+\left (-2 b -4 c +4 d -4 e \right ) a +b^{2}}}{2 a}\right ], \frac {\cos \left (x \right )}{2}+\frac {1}{2}\right ) c_{1}+\cos \left (\frac {x}{2}\right )^{\frac {2 a +\sqrt {a^{2}+\left (-2 b -4 c +4 d -4 e \right ) a +b^{2}}}{2 a}} \operatorname {hypergeom}\left (\left [\frac {\sqrt {a^{2}+\left (-2 b -4 c -4 d -4 e \right ) a +b^{2}}+2 i \sqrt {4 a c -b^{2}}+\sqrt {a^{2}+\left (-2 b -4 c +4 d -4 e \right ) a +b^{2}}+2 a}{4 a}, \frac {\sqrt {a^{2}+\left (-2 b -4 c -4 d -4 e \right ) a +b^{2}}-2 i \sqrt {4 a c -b^{2}}+\sqrt {a^{2}+\left (-2 b -4 c +4 d -4 e \right ) a +b^{2}}+2 a}{4 a}\right ], \left [\frac {2 a +\sqrt {a^{2}+\left (-2 b -4 c +4 d -4 e \right ) a +b^{2}}}{2 a}\right ], \frac {\cos \left (x \right )}{2}+\frac {1}{2}\right ) c_{2}\right )\]