It is well known that if we allow for large oscillations the equation for a simple pendulum,
$$ \begin{equation*} \frac{\mathrm{d}^2\theta(t)}{\mathrm{d}t^2}=-\omega^2\sin\theta(t), \end{equation*} $$
can be solved in terms of elliptic integrals. Furthermore, if we allow for a frequency changing with time (not a dynamical variable but an specified function), i.e.,
$$ \begin{equation*} \frac{\mathrm{d}^2\theta(t)}{\mathrm{d}t^2}=-\omega^2(t)\sin\theta(t), \end{equation*} $$
I know no solutions reported in the literature even for simple forms of $\omega$ like polynomials. Since the variable $t$ is explicit through $\omega^2(t)$ then the equation is no longer an autonomous equation, and we may a priori say that there is no easy or evident change of variable or substitution that allows for an integration. I would like to know if there are particular cases or methods suited for such an equation.