Physical conditions in the analytical solution on the Mathieu equation

The study aims to analyze the Mathieu equation associated with linear systems under properties, use the one-dimensional Floquet theorem and explain the behavior of the solutions of the Mathieu equation and function relating to the Hill equation together with the theory of disturbances. The most common mathematical problem in physics is finding solutions to certain second-order differential equations subject to boundary conditions. A hypothetical deductive approach method, handling qualitative equations of mathematical physics, was adopted in review. With Mathieu's equation, the existence of the physical conditions that influence the value of the parameters that define the equation were answered. It is important due to its usefulness in the field of analytical and mechanical dynamics, physical systems subjected to parametric excitation; In addition, it leaves other variations open for new applications.