Undergrad Classification of First Order Linear Partial Differential Eq

[Ali Baig]

How can I classify a given first order partial differential equations?
Are all first order linear PDEs hyperbolic?
Quora Link:https://www.quora.com/How-do-I-clas...-or-parabolic-using-method-of-characteristics

 

[Simon Bridge]

Not all linear first order PDEs are hyperbolic, no.
The Quora post you point to actually spells that out... the author says that some are elliptical etc.

You classify a PDE according to the definitions of the classes... for that detail, you need a good reference on PDEs.

Turns out to be an easy Google (use, "classifying PDEs") to get for instance: