Reddit reviews Differential Equations and Boundary Value Problems: Computing and Modeling (5th Edition) (Edwards, Penney & Calvis, Differential Equations: Computing and Modeling Series)

313's difficulty level is to a large extent dependent on your comfort with previous math classes, and with your comfort with the concept of mathematical structures. If 313 is your first formal experience to mathematical structures, it will likely be much more difficult. If you are already familiar with concepts such as sigma algebras, measurable spaces, etc., it will likely be a significantly easier class.

Linear algebra, though not being necessary to understand the material the way multivariable calc is, will help you understand the material.

Covariance, which is a topic discussed towards the end of the semester and which measures the linear dependence of two random variables, is very similar to an inner product from linear algebra. Covariance shares the bilinear, symmetric, and positive semi-definite properties with an inner product. Covariance also adheres to the Cauchy-Schwartz inequality.

In addition, the class discusses linear and non-linear one-to-one transformations of systems of random variables. These two sections, which were generally considered to be quite difficult, are actually quite easy if you have a solid understanding of linear algebra.

That being said, I don't know how relevant MATH 286 would be for this class. Maybe someone who's taken MATH 286 wants to chime in on how much linear algebra you actually learn in that class. Looking at the MATH 286 textbook's table of contents, it looks like you will likely learn how to find the eigenvalues and eigenvectors of a matrix, but not actually learn why or how or what is really going on.

ECE 313 forces you to use office hours due to the "concept matrix". But really, if you take the time to actually learn the concepts - why you're applying a formula, not just how to apply a formula - you should do just fine in the course.