Hyperbolic Linear PDE

Subject:

Consider the following second-order linear partial differential equation(PDE)in two varibles:

Auxx+ Buxy + Cu yy + Dux + Euy + Fu = G(x,y) ----(Eqn 1)

Where A, B, C, D, E, F and G can be constants or functions of x and y.

The above PDE (eqn 1) is hyperbolic if B2 - 4AC > 0. Hyperbolic PDE describe wave motion and vibrating systems.