My university's cybersecurity program allows one to take a course in ordinary differential equations as an elective. The course would be interesting to take, although I don't know how I'd apply it to anything. Are there any examples of cybersecurity problems that are solved with ODEs?
I don't want to say definitively no, but trigonometry, calculus (including ODEs) doesn't come up much in cryptography or cyber-security. That said its still part of a basic STEM background mathematical literacy, so I'd personally recommend taking the course just as part of a standard breadth of general education.
There are two examples I can come up with. First, is some CS topics that could be of relevance to a cyber-security expert, will at times involve differential equations in the theory behind it -- specifically with Machine Learning and Artificial Intelligence. Granted, its not going to be solve
y'' + 3y' + 1 = exp(2 x) type things you'll learn to solve in a typical ODE class. It's more just being comfortable with the basic concept of differential equations. For example, browse the lecture nodes to the Stanford version of Andrew Ng's ML class).
The other example is if for your cyber-security needs require you knowing some physics, which frequently will involve differential equations. E.g., if you need to understand the physics of wireless transmission.
That said, its more relevant learning basic number theory and linear algebra. Somewhat relevant: is this question "What is the lowest level of math needed in order to understand encryption".