I am having a lot of trouble understanding the method of characteristics to solve the wave equation.
In fact, I have a final exam tomorrow and I can't seem to get a question from a previous assignment. I know Math.SE isn't really meant for this kind of stuff but I am hoping someone would just briefly explain how my professor is getting the solution. I appreciate it.
Here is the problem: $\frac{\partial^2 u}{\partial t^2} - 9 \frac{\partial^2 u}{\partial x^2} = 0$ on the real axis (i.e., $-\infty < x < \infty$).
Here is the solution. It is a PDF to the professor's solution file.
The solution is on page 3 (question number 3).
I need to know how he's getting his solutions at different times.