What class comes after Linear Algebra and Differential Equations

It pretty much branches out to whatever you want to do in math. At some point, you probably want to take an Real Analysis class and a Modern (aka Abstract) Algebra class.

You could take some fascinating classes in discrete math like Combinatorics, Graph Theory, and Number Theory.

Then there's also Topology, Complex Analysis, and Partial Differential Equations, and loads more even at an undergraduate level.

The natural progression would be real analysis or probability theory.