Analytical Solution for the two-dimensional wave equation, separation of variables
The second step is to solve these differential equations, which all have trigonometric functions as solutions, viz.
$$
\begin{equation*}
H(x) = A\cos(\kappa x)+B\sin(\kappa x),
\end{equation*}
$$
and
$$
\begin{equation*}
Q(y) = C\cos(\rho y)+D\sin(\rho y).
\end{equation*}
$$