FUNDAMENTAL SOLUTIONS ABOVE EQUATIONS OF THE PARAMETRIC OSCILLATIONS
Journal Title: Збірник наукових праць Українського державного університету залізничного транспорту - Year 2017, Vol 167, Issue 1
Abstract
We define the fundamental solution of the Mathieu equation for zero setting a and arbitrary parameters q using the method of direct integration. Along with the original Mathieu equation is considered tantamount to his system of equations. Fundamental solutions obtained in the form of a power series. It is built the fundamental matrix of solutions of the equivalent system equations. It is shown that this matrix is unambiguously determined and is matriciant. The general solution of equivalent systems of differential equations is expressed by the well-known formula matriciant, where we obtain the general solution of the original Mathieu equation.
Authors and Affiliations
Yuriy Krutiy, Nikolay Suryaninov
Keywords
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