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I have boiled a very long physics problem down to the point that I need to solve the coupled equations

[tex] \frac{\partial^2 x}{\partial u^2} + xf(u) + yg(u) = 0 [/tex]

[tex] \frac{\partial^2 y}{\partial u^2} + yf(u) - xg(u) = 0 [/tex]

We may assume that[tex] |f| ,|g| << 1.[/tex] and that both f and g are periodic on the same interval T, i.e. [tex]f(u) = f(u+T),g(u) = g(u+T)[/tex]

I was wondering if this is something that could be solved with little knowledge of perturbation theory or if this was a very advanced problem, and I was wondering if anyone had any useful resources. So far I have found that this would be relatively easy to solve if they weren't coupled, but this is a level of complexity which is beyond me

Thank you.

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# Can a basic knowledge of perturbation theory solve this?

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