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Linearization methods play a very important role in the study of nonlinear systems which are generally modeled by nonlinear ordinary differential equations. Although many systems can admit a domain of linear behavior, linearity is always an approximation of reality. The most classic approximation is that determined by the derivative in the Fréchet sense of the nonlinear equation. Due to the diversity and power of the tools developed in the linear domain, it is usual initially to linearize the nonlinear model around an operating point and to use the linear model thus obtained in order to extract as much information as possible.The object of this work is the analysis of a non-linear physical system from electronics as well as the use of certain tools specifically developed in this context.We applied the optimal derivative method to a physical system of an electronic motor circuit. This system is described by nonlinear ordinary differential equations. We are interested in the study of the asymptotic stability of this system. The approximation obtained by optimal derivation gives satisfactory results compared to the exact results while respecting the dynamics of the initial problem.