>>10569416DEs are the setting in which great fun stuff like functional analysis is often used
also there's plenty of reasons to know DEs, from dynamical systems to differentiable manifolds to complex analysis, etc etc.
pretty much any analysis class makes use of the core material in an introductory DEs class.
don't bother learning how to solve them, but knowing why existence-uniqueness works, knowing about continuity on initial conditions, linearization and phase plots of linear systems, tools for solution such as fourier series and transforms, and so on, is so deeply important to mathematics as a whole that you're doing yourself a huge disservice by ignoring it.
