I've been set the question above, and I'm having some problems on where to start. I haven't come across PDE's in more that two dimensions before so I'm quite confused.
I started by trying to use d'Alembert's formula for this given v however first of all I thought that d'Alemberts formula only worked in two dimensions furthermore, say we could apply d'Alembert in $\mathbb{R}^3$ then determining u from our definition of it and v(x,t;s) = $\frac{1}{2c}\int^{x+t}_{x-t}$f(y,s)dy seems unfindable. I also tried determining u$_{tt}$ and u$_{xx}$ immediately however I couldn't find a viable way to do so with what I had been told in the question.
I won't be marked on this question however I would still prefer to not be given the answer to it. These equations I've been told will be relevant in my finals hence I would rather someone explain where to start on this question and I will try to complete the rest myself.