Cyclic Functions under Differentiation

This Demonstration explores functions (such as sine and cosine) that are cyclic under differentiation with period four. Such a function is uniquely determined by its value and first three derivatives at a point. The thick curve is the cyclic function itself, and the dotted curves are the first four truncations of its Maclaurin series.

SNAPSHOTS

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DETAILS

An cyclic function is defined as a solution of .
This is an explicit form for a fourth cyclic function:
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