We used the Boyce and DiPrima book back when I was an electrical engineering student (Elementary Differential Equations and Boundary Value Problems https://www.amazon.com/Elementary-Differential-Equations-Bou...).

I remember it was an excellent book with many great examples and correlation with physics topics like mechanics, waves etc. Too bad our other mathematics books weren't at this high standard :/

Also, I really don't think that such topics can be self-studied. It seems really difficult to me to understand such topics without a teacher!