On the transformation of the linear differential equation into a system of the first order equations
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 o...
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| Date: | 2019 |
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| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2019
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| Series: | Вопросы атомной науки и техники |
| Subjects: | |
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/195169 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | On the transformation of the linear differential equation into a system of the first order equations / M.I. Ayzatsky // Problems of atomic science and technology. — 2019. — № 4. — С. 71-75. — Бібліогр.: 22 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | 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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