Consider following PDE:
$u_{xx} - u_{tt} = 2u_t$
And $u$ is a function of $t$ and $x$. This is an example of hyperbolic equation. Using change of variables $v = t - x$ and $w = t + x$, equation becomes:
$u_{wv} = \frac{-1}{4}(u_v + u_w)$
I don't know how to proceed further with this. Twice integration doesn't work. So it means that characteristic method doesn't work at all for this problem?