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

M. I. Ayzatsky

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

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arxiv 1803.03124 v3 pith:F4UHTABT submitted 2018-03-06 math.CA

M. I. Ayzatsky This is my paper · ORCID

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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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