Express the 2nd order ODE
$\begin{align}\mathrm d_t^2 u:=\frac{\mathrm d^2 u}{\mathrm dt^2}&=\sin(u)+\cos(\omega t)\qquad \omega \in \mathbb Z /\{0\} \\u(0)&=a\\\mathrm d_t u(0)&=b\end{align}$
as a system of 1st order ODEs and verify there exists a global solution by invoking the global existence and uniqueness theorems.
I'm not sure how to express second order ODEs as first order ODEs, any tips?