I'm just trying to get an understanding of answering PDEs, so wanted to ask what you thought of my answer to this question.
The one-dimensional wave equation is given by the first equation shown in this link;
where Ψ = f(x, t)
Is f(x, t) = cos(x-vt) + (x-vt) a possible solution?
∂^2 f/∂x^2 = -cos(x-vt)
∂^2 f/∂t^2 = c^2 cos(x-ct)
So, since -cos(x-vt) ≠ cos(x-vt) I assume this is not a solution.