Need help proving that a function is a solution to the homogeneous wave equation

[JerryG]

Homework Statement

I have a homework problem that says that any function of the below form is a solution to the homogeneous wave equation.

Any function of this form is a solution to the following equation:

I would be able to solve it if the function was defined, but I'm not quite sure how to handling the partial differential equations using this general solution.

 

[fzero]

Let $$y = t -R\sqrt{\mu\epsilon}$$ and use the chain rule on $$U(R,t) = f(y)$$.

 

[dextercioby]

Didn't you take a math course showing you the reverse ? Well, checking if a certain function obeys a differential equation is a piese of case comparing to solving the equation to obtain that function as solution/among all solutions.