Abstract
This chapter presents Mathieu's general equation. The terms stable and unstable arise naturally from the frequent occurrence of Mathieu's general equation in problems where z represents time. Stability or instability is a property of the general solution and so intrinsic in the equation itself and dependent only on the values taken by q and a. The standard form of Mathieu's equation is taken to be (d2w/dz2) + (a − 2q cos 2z)w = 0, and the result of writing iz for z is the modified Mathieu equation. Stability or instability is a property of the general solution and so intrinsic in the equation itself and dependent only on the values taken by q and a.
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