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Exact solution of the quadratic mixed-parity Helmholtz-Duffing oscillator. (English) Zbl 1245.34002
Summary: The exact solution of the quadratic mixed-parity Helmholtz-Duffing oscillator is derived by using Jacobi elliptic functions. It is also shown that the exact period of oscillation is given as a function of the complete elliptic integral of the first kind. At the end of the paper, we examine the stability of the system and determine the regions for which periodic and unbounded motions take place.

MSC:
34A05 Explicit solutions, first integrals of ordinary differential equations
34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
34C25 Periodic solutions to ordinary differential equations
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