Actually, the way that I was taught (and teach) is to consider the form
(lots - lower order terms)
Just like classifying quadratics
I'm reading a textbook that tells me that if we have a general linear homogeneous pde of 2nd order:
we can create a matrix A, where
and use it to classify the PDE as follows:
Elliptic: Det i.e.
which seems fairly simple enough. But in the examples they have, I get something completely different to the solutions they provide.
(a) . I get so Det
I get and Det
I get and det
According to the text these should be
(a) Det A = -9/4
(b) Det A = 0
(c) Det A = 5
but I get something different.
Also, as another example, we have
and we should have Det . Where is the coming from?