Jacobi Elliptic Functions As Solutions of Nonlinear Ordinary Differential Equations
The derivatives of the three basic Jacobi elliptic functions are:
With the addition theorems above and for a given k with 0 < k < 1 they therefore are solutions to the following nonlinear ordinary differential equations:
- solves the differential equations
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- and
- solves the differential equations
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- and
- solves the differential equations
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- and
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