We're studying systems of linear differential equations (or vector-valued differential equations) in my class right now. Since linear algebra isn't an official prerequisite for the class, I've had to give a crash course in matrix algebra and eigenvectors during lecture. I think I've succeeded in going in enough detail to bore everybody who's taken linear algebra, but briefly enough that the students who haven't taken linear algebra are still confused. Win-win, baby.
But seriously, I think it's a better idea to leave systems of DEs for a linear algebra class. The time could be spent looking at Laplace transforms or numerical solutions -- these are tools that are more useful to a wider audience, I think. Anybody who needs to know about systems of DEs probably also needs a full course in linear algebra, and it's easier to teach DEs in a linear algebra class than it is to teach linear algebra in a DEs class.