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I've been looking for the form of the solution(s) to following differential equations:

[itex]\frac{\partial^2}{\partial x \partial y}f(x,y) = a \cdot g(x,y) [/itex]

[itex]\frac{\partial^2}{\partial x \partial y}g(x,y) = b \cdot f(x,y) [/itex]

Where a and b are unrelated constants, and f,g are of the same general form. I've tried exponentials and different categories of Bessel functions, with no luck. Does anyone recognize what form the solution(s) might take? Or have an idea of how I could proceed to solve this?

Thanks in advance :)

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# Unknown Solution Form

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