So I'm working on a solution to this PDE,
I started by classifying the PDE and found it to be hyperbolic. So, I attempted to reduce it to canonical form, making the substitutions
Then, I obtained that
Substituting this back into the PDE, I end up with the equation
At about this point, I'm getting stuck on finding a general solution to the PDE by simplifying it further. I suspect the problem is with my substitution, specifically with , but I'm not really sure what's wrong with it, other than it looking a bit suspect. Can anyone point me in the right direction?