- Thread starter
- #1

Show that the equation $$u_{tt} - c^2 u_{xx} + au_t + bu_x + du = f(x,t)$$

can be transformed into an equation of the form

$$w_{\xi\tau} + kw = g(\xi,\tau), w = w(\xi,\tau)$$

by first making the transformation $$\xi = x - ct, \tau = x + ct$$ and then letting $$u = w\exp{\alpha\xi + \beta\tau}$$ for some alpha and beta

I'm completely stumped at how to solve this problem, but I do not expect a solution, only a way to begin so I can get used to problems like these in general.