Open AccessON THE TRANSFORMATION OF THE LINEAR DIFFERENTIAL EQUATION INTO A SYSTEM OF THE FIRST ORDER EQUATIONS
Author(s) -
M. I. Ayzatsky
Publication year - 2019
Publication title -
problems of atomic science and technology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.216
H-Index - 17
eISSN - 1562-6016
pISSN - 1682-9344
DOI - 10.46813/2019-122-071
Subject(s) - riccati equation , independent equation , linear differential equation , first order partial differential equation , differential equation , mathematics , transformation (genetics) , homogeneous differential equation , nonlinear system , mathematical analysis , order (exchange) , generalization , partial differential equation , ordinary differential equation , differential algebraic equation , physics , biochemistry , chemistry , finance , quantum mechanics , economics , gene
The generalization of the transformation of the linear differential equation into a system of the first order equations is presented. 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.