How Does u(x,t) = F(x+ct) + G(x-ct) Satisfy the Wave Equation?

[malt life]

Homework Statement

struggling with a problem and hoping someone could help me out. the problem reads,

Let F and G be arbitrary differentiable functions of one variable. Show that u(x,t) = f(x+ct) + G(x-ct) is a solution to the wave equation, provided that F and G are sufficiently smooth.

thanks in advance

Homework Equations

The Attempt at a Solution

 

[lanedance]

i'd start with the wave equation