Hello. This is my problem:

Let A,B and C be positive constants and the hyperbolic partial differential equation: Au_{xx}+Bu_{xy}+Cu_{yy}=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:

u_{xx}=a^{2}f_{xx}+a^{2}g_{xx}

u_{xy}=abf_{xy}+abg_{xy}

uyy=b^{2}f_{yy}+b^{2}g_{yy A}a^{2}f_{xx}+Aa^{2}g_{xx}+Babf_{xy}+Babg_{xy}+Cb^{2}f_{yy}+Cb^{2}g_{yy }= 0

But I am not sure how to continuate. Any idea?? Thanks