\[ y''(x)=-\cot (x) y'(x)-\frac {1}{4} y(x) \left (-17 \sin ^2(x)-1\right ) \csc ^2(x) \] ✓ Mathematica : cpu = 0.0638446 (sec), leaf count = 37
DSolve[Derivative[2][y][x] == -1/4*(Csc[x]^2*(-1 - 17*Sin[x]^2)*y[x]) - Cot[x]*Derivative[1][y][x],y[x],x]
\[\left \{\left \{y(x)\to \frac {c_1 e^{-2 x}}{\sqrt {\sin (x)}}+\frac {c_2 e^{2 x}}{4 \sqrt {\sin (x)}}\right \}\right \}\] ✓ Maple : cpu = 0.042 (sec), leaf count = 22
dsolve(diff(diff(y(x),x),x) = -1/sin(x)*cos(x)*diff(y(x),x)-1/4*(-17*sin(x)^2-1)/sin(x)^2*y(x),y(x))
\[y \left (x \right ) = \frac {c_{2} \cosh \left (2 x \right )+c_{1} \sinh \left (2 x \right )}{\sqrt {\sin \left (x \right )}}\]