# Math Help - 2nd Order Linear PDE Canonical Form Query

1. ## 2nd Order Linear PDE Canonical Form Query

Folks,

I am trying to see a pattern when solving 2nd order linear PDE's.

The canonical form for the Hyperbolic case is

$\bar B w_{st}+ \phi(w_s,w_t,s,t,w)=0$ where $\bar B \ne0$

If the discriminant is a real number does the $\phi$ term vanish and hence if the discriminant is some $f(x,y)>0$, do we always have some $\phi$ terms?

And similarly for the elliptical case?

Thanks

2. ## Re: 2nd Order Linear PDE Canonical Form Query

Generally speaking there will be lower order terms. Sometimes (if you're lucky) you can integrate your transformed PDE once or even twice.