Yes there is! This needs to be highlighted so that nobody misses the memo:

The theory of Jet Bundles = The general theory of differential equations.

It is the mathematical formalism that provides a general and universal framework for both ordinary and partial differential equations.

A standard application of Jet Bundles is that of finding the symmetries of a set of equations that may include ordinary algebraic equations (i.e. order 0 differential equations), ordinary and/or partial differential equations within it. Here's an example: find the Symmetry Group Of Newton's First Law (It's SL(5)).

Now, here's a question that expands on the issue: is there a general framework for differential equations - including non-linear ones - for non-commutative algebras and/or generalized functions? For instance, is there a non-commutative or distributional version of Jet Bundle theory? There is such a thing as Non-Commutative Geometry, though I don't know if that's the place where non-commutative differential equations live.