Let $A, B, C\geq 0$ be constants. Is there an explicit formula to a nontrivial solution to the homogeneous linear ODE $$y''(t) -(A+B\,\sin t)\,y'(t) -C\, y(t)=0$$ for $t\in(0,2\pi)$ with periodic boundary condition $y(0)=y(2\pi)$? This is not clear to me even for the case $A=0,B=C=1$. Thanks!