Classifying a second-order PDE, and the type that changes

Partial Differential EquationsODE, PDE & Applied Mathematicsfree

One discriminant decides everything — including equations that are elliptic in one region and hyperbolic in another.

Step 1 / 4The discriminant

For $A u_{xx} + B u_{x y} + C u_{y y} + \dots = 0$ , compute $B^{2} - 4 A C$ :