Differential equations is definitely used as one of the filters in engineering courses. It pretty quickly sifts people who never really grasped the basics of calculus and algebra.
That said, Fourier transforms aren't terribly difficult. In fact, by the time you get Fourier transforms you're happy to see something that's going to make your life easier. Just make sure you understand algebra and calculus. To be fair if you're American we're notoriously bad at teaching math, and our math literacy is well below what's considered to be proficient. We also have a culture where not knowing basic math skills like algebra is acceptable and just means "ur not one dem nerds".