Suppose we have the following non-linear differential equation
where $x(t)$ is a function of time $t$ a and where we choose $\omega^2(t)$ to be some (positive) periodic function, to be more specific, let us say
with $\omega_1$ and $\omega_2$ being positive constants.
Let us choose $\omega_1=1$ and $\omega_2=2$, and the initial conditions e.g. $x(0)=1$, $x'(0)=1$.
How to approach the solution in Mathematica?