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Usually for second order differential equations, we get a general solution with 2 constants that are obtained by using the boundary conditions. What about for a coupled pair of second order differential equations? Would I be right to think that the same applies?

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You will have $4$ constants, which can be taken as the values of the dependent variables and their derivatives at the initial point.

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Dear Robert, thank you. – marius Apr 1 '12 at 19:56

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