ON THE TRANSFORMATION OF THE LINEAR DIFFERENTIAL EQUATION INTO A SYSTEM OF THE FIRST ORDER EQUATIONS | Zendy

M. I. Ayzatsky | Zendy

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ON 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.

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