What is the relationship between A and B in the given equation?

[PassThePi]

Homework Statement

E = [axhat(A(x+y)) = ayhat(B(x-y))]cos(wt)

Determine the relationship between A and B

Homework Equations

I don't know if there are any.

The Attempt at a Solution

I've expanded the problem and reduced it to E = cos(wt)[x(A+B)axhat + y(A-B)ayhat]
I was going to take the real component and convert to the frequency domain to try to manipulate the cosines but I don't know if that's the right step.

If someone could just get me started or point me in the right direction I think I could figure it out. Not looking for someone to do this for me.

 

[fzero]

It would help to know what E represents. Is it supposed to be a solution to the wave equation or some other pde? If so, you can try to apply that equation and find conditions on A and B. If E is an electric field, there is an additional condition on its divergence that might be useful.

Also, it seems likely that A(x+y) and B(x-y) are meant to be functions of those arguments, so the rearrangement that you made is probably incorrect.