An analytical coupled homotopy-variational approach for solving strongly nonlinear differential equation

In the present paper, a novel technique combining the homotopy concept with variational formula has been presented to find accurate analytical solution for nonlinear differential equation with inertia and static non-linearity. The obtained results are compared with other analytical and exact solutions to confirm the excellent accuracy and correctness of the approximate analytical technique. The results of the present paper are valid for large amplitudes of oscillation; also the approximate solutions give excellent result than other methods. We concluded that the first order approximation obtained in current work are almost the same with exact solutions, also works very well for the whole range of initial amplitudes.