Linear algebra is 50% really cool shit and 50% completely useless shit. The annoying part about learning it is that most new concepts are introduced as a set of axioms that don't immediately seem very useful. Lots of topics like vector spaces, inner product spaces, and eigenvectors fall under this category where they don't seem useful until they're utilized much later for an unexpected purpose. One of my personal favorite standard topics in linear algebra is where you can develop a Fourier series for any function by showing that sin(kx) is an orthogonal set. It's a completely unexpected and beautiful use of concepts which are taught much earlier in the course.
There's a lot of bullshit in the class too though. QR factorizations are a standard topic in the class, and are used later in numerical analysis for their purported use of solving equations. For all they talk up their usefulness though I've never once seen a situation where a QR factorization seemed like a good solution to a problem. Your mileage may vary with this because it seemed like something that pairs very well with computers. Making people do it by hand is exceptional and counterproductive, especially iterations of it.
Differential equations wasn't that bad for me, but I immediately forgot everything it teaches. What I took out of that class is that Laplace transforms are good and everything else is black magic. I took that before I took linear algebra and I utterly regret that decision. There's a lot from linear algebra that can be applied to diff eqs, but hardly anything from diff eqs can be applied to linear algebra. Matrices are like training wheels for solving differential equations, but once you've learned diff eqs before matrices it doesn't help at all.
![:\](/styles/custom/emotes/svg/chris-confused.svg "Confused :\")
