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Analytical solution of the damped Helmholtz-Duffing equation. (English) Zbl 1259.34004
Consider the differential equation \[ \ddot x+ Ax+ 2\nu\dot x+ Bx^2+\varepsilon x^3= 0.\tag{\(*\)} \] Under the assumption \(A= {3B^2+ 8\varepsilon\nu\over 9\varepsilon}\), the author derives an analytic solution of equation \((*)\) by using Jacobian elliptic functions.

MSC:
34A05 Explicit solutions, first integrals of ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems, general theory
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