I asked this in the board for HA3 P3 as well but I am cross-posting here.
Just wondering, is there a typo in the original problem? The equation given is: \begin{equation}
Au_{tt} + 2Bu_{tx} + Cu_{tt} \end{equation}
But I think the last term should be with respect to x: \begin{equation}
Au_{tt} + 2Bu_{tx} + Cu_{xx}
\end{equation}
Indeed, corrected