In general a second order linear [[Partial differential equations|PDE]] has the form $A\partial_{xx}+ B \partial_{xt}u+C\partial_{tt}u +G(u, \partial_{x} u, \partial_{t}u)=0$where $A,B,$ and $C$ are constants. Like in [[Reduction of the general second degree equation]], we can reduce the *principal part*, $Ax^{2}+Bxy+Cy^{2}$, to one of the following canonical forms: - $x^{2}+y^2$ - elliptic - $x^{2}-y^{2}$ - hyperbolic - $x^2$ - parabolic