so it's hyperbolic. This means under a change of variable we should be able to transform you PDE to a standard form, i.e.
(I'm using r and s instead of and . lots - lower order terms). We now introduce first and secord order transforms. If then
Substitute these into your PDE and group terms
In order to hit the target we need the coefficient of and to vanish. Thus,
They are the same so choose one for and the other for , i.e.
These are first oder PDEs, so by the method of characteristics, we fiind the solutions
which we choose the function and simple. So
(as you said).
Now put these into your transformations (1) and put all of these into you PDE and simply. See how that goes.