Hello. This is my problem:
Let A,B and C be positive constants and the hyperbolic partial differential equation: Auxx+Buxy+Cuyy=0. Get a general solution of the form:
u(x,y) = f(ax+by)+g(ax+by) where a,b,c,d are real constants and f and g are C2 functions.
Well, I have started computing the derivatives of the given solution and putting them into the equation:
Aa2fxx+Aa2gxx+Babfxy+Babgxy+Cb2fyy+Cb2gyy = 0
But I am not sure how to continuate. Any idea?? Thanks