Differential equations is really essential knowledge here, at least if you want to understand how rate laws are derived. I don't think you necessarily need an entire course on the subject, though. Most physical chemistry books include a basic treatment of the subject, so unless you intend to study chemical kinetics in graduate school and beyond, what you get in a standard Pchem class will probably be sufficient to do OK at the undergraduate level in my opinion.
(Basic integral calculus on the other hand you really need to know backwards and forwards for physical chemistry. It really comes into play everywhere.)