Solution (source code)

= Solution

With $\xi=x-ct$, time <derivatives> become $-c$ times $\xi$ <derivatives> and $I_{xx}=I''$. Hence
$$
\boxed{-cS'=-IS,}
$$
$$
\boxed{-cI'=I''+IS-\mu I,}
$$
or equivalently
$$
cS'=IS,
\qquad
I''+cI'+(S-\mu)I=0.
$$