[xxxtentachyon]

I wouldn't really expect them to be able to solve a simple ODE with just Calculus BC. It's been about a decade since I took it, but to my memory, it concluded with basic elements of real analysis after getting pretty far along with single variable integral calculus techniques. We never discussed ODEs as such, but some clever students would probably recognize how to solve them on sight without being acquainted with the broader fields of differential equations