Is There a Subset of the General PDEs?

A very big chunk of the ones that we know are directly related to like physics or like real world issues, like finance or problems that we have to deal with in real life. Most of them we've solved and if they don't then well, there are other ways to solve it. There's so many different techniques to integrating systems which is a whole field on its own. But I'm saying right now with what we know, at least most of the partial differential equations, I think, solutions.