Analytical solution of a nonlinear oscillator by the linearized perturbation technique

In this paper, a nonlinear oscillator with no possible small parameters is considered. The traditional perturbation techniques can not be applied to such a problem. By linearizing the nonlinear system, and embedding an artificial parameter, we obtain an approximate solution which is valid on the whole solution domain, and the results are in remarkable agreement with the exact one even in the case where the amplitude of the oscillator tends to infinite.