This paper introduces a novel complexdisplacement-velocity method (CDVM) based on thedisplacement and velocity complex variables, whichis compared with the multiple scales method (MSM)when applied to the Duffing oscillator under a seventhorderaeroelastic galloping force. Furthermore, we obtainthe approximate solutions by using CDVM andcompare them to those obtained by the MSM. TheRaphsen-Newton method is employed to solve the obtainedpolynomial equations for steady states, confirmingthe validity of the proposed method through numericalsimulations. The stability chart is establishedby utilizing the Jacobian matrix of slow-flow equations.