These sorts of classes tend to get students in a broad range of levels, and I think there's the expectation that they'll figure out whatever they're unfamiliar with. I doubt this class is targeted to graduate students, but Caltech classes tend not to have a graduate/undergraduate distinction.

difeq is part of the common core that everyone must take to graduate and taught to sophomores first term, although a few (maybe 10-15 or so each year? out of about 200-250) (as of about a decade ago) students will test out of ma1a and then take ma2a first term freshman year instead of sophomore year. Testing out of ma1a requires knowing both calculus and also proof techniques.

courses numbered 100-199 are taken by both undergrads and graduate students, and because of Caltech's "rigorous" core often (but not always) the undergrads have an easier time.

I don't know this class specifically, but you would probably have a couple super motivated sophomores but mostly juniors and seniors taking a course numbered like this. Occasionally a few people will take 100-level courses freshman year (I took one such full-year and 1 one-term class, and I wasn't the only frosh in either).

(humanities/social science courses numbered 100+ are a bit of a different matter and tend to be super easy, but no one really takes those classes seriously for obvious reasons)