A note on the transformation of the linear differential equation into a system of the first order equations
Classical Analysis and ODEs
2018-04-20 v3
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.
Keywords
Cite
@article{arxiv.1803.03124,
title = {A note on the transformation of the linear differential equation into a system of the first order equations},
author = {M. I. Ayzatsky},
journal= {arXiv preprint arXiv:1803.03124},
year = {2018}
}
Comments
10 pages, 0 figures, Formulas (58)-(64) in Appendix were replaced by the correct ones