I'm looking for a nice reference on the Frobenius Theorem. Ideally, I'd like to find a reference that's going into detail on its various forms (vector fields/differential forms) and has a lengthy discussion on applications in PDE theory. I'm currently using Lee's Smooth Manifolds book, which I find to be "just okay" for this topic. I have several differential geometry/topology and PDE texts, yet I can't find Frobenius in any of them.

Any help would be greatly appreciated,