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:<math> \frac{d^2y}{dx^2}+[a-2q\cos (2x) ]y=0 </math>
The Mathieu functions are used in treating problems involving [[parametric resonance]], vibrating elliptical drumheads, and gravitational waves in [[general relativity]], among other applications. They were introduced by [[Emile Mathieu]] in [[1868]] in the context of the second problem.
==Floquet solution==
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