A note on the transformation of the linear differential equation into a system of the first order equations

2018/03/06 by M. I. Ayzatsky, Ayzatsky, M. I.
Physics and Astronomy · Mathematics · #Nonlinear Waves and Solitons #Numerical methods for differential equations #Fractional Differential Equations Solutions

paper · pdf · doi:10.48550/arxiv.1803.03124

Abstract

A generalization of the already studied transformations of the linear differential equation into a system of the first order equations is given. The proposed transformation gives possibility to get new forms of the N-dimensional system of first order equations that can be useful for analysis of the solutions of the N-th order differential equations. In particular, for the third-order linear equation the nonlinear second-order equation that plays the same role as the Riccati equation for second-order linear equation is obtained.

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