1. ## d'Alembert's formula

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.

2. ## Re: d'Alembert's formula

Two thoughts. First, if you allow that $c = a$, then you already have the form. Second, if you let

$k_1(x+ct) + k_2(x-ct) = x - at.$

If you expand and equate like terms, you'll find two equations for $k_1$ and $k_2$.

3. ## Re: d'Alembert's formula

If I were you, I would start by stating d'Alembert's formula as clearly as possible.