  In this work, we present a method of generating a class of nonlinear ordinary
differential equations (ODEs), representing the dynamics of appropriate
nonlinear oscillators, that have the characteristics of either amplitude
independent frequency of oscillations or amplitude dependent frequency of
oscillations from the integrals of the simple harmonic oscillator equation. To
achieve this, we consider the case where the integrals are in the same form
both for the linear and the nonlinear oscillators in either of the cases. We
also discuss the method of deriving the associated integrals and the general
solution in harmonic form for both the types. We demonstrate the applicability
of this method up to 2N coupled first order nonlinear ODEs in both the cases.
Further, we illustrate the theory with an example in each case.
