posted by Margo .
Show that u(x, t) = f(x−ct)+g(x+ct), where c is a constant and f and g have continuous second derivatives, is a solution of the wave equation in
one dimension, ie (∂t)^2 u = c^2 ∂x^2 u. Note that this solution to the wave equation consists of two functions who keep the same shape but travel to the left and right with speed c.
so, do you have a problem taking the partials and showing that they fit the equation?