Solution of the Duffing Helmholtz Oscillator Equation by Elementary Functions with Physics Applications

In this article we give a new analytical solution to the Duffing-Helmholtz oscillator equation in terms of elementary functions. The solution obtained is compared with the numerical solution and with the exact analytical solution obtained using elliptic functions. We apply the obtained results to some physics problems. The proposed methodology may be of great interest to researchers in the field of nonlinear oscillators.