Good morning all, I am stuck on this question.
Use d'Alembert's formula to write u(x,t) = x-at in the form u(x,t)=f(x+ct)+g(x-ct).
I don't know how to do this so any help would be very nice.
Thanks.
Two thoughts. First, if you allow that $\displaystyle c = a$, then you already have the form. Second, if you let
$\displaystyle k_1(x+ct) + k_2(x-ct) = x - at.$
If you expand and equate like terms, you'll find two equations for $\displaystyle k_1$ and $\displaystyle k_2$.