ON THE INTEGRABILITY OF A CLASS OF DIFFERENTIAL EQUATIONS

Authors

  • Biljana Zlatanovska Goce Delcev University image/svg+xml Author
  • Boro M. Piperevski Ss. Cyril and Methodius University in Skopje image/svg+xml Author

DOI:

https://doi.org/10.37560/matbil21452085z

Keywords:

Second-order linear differential equations, system of first-order differential equations, particular solution

Abstract

In this paper, a class of second-order linear differential equations is reviewed. For this class of B.S.Popov necessary and suffcient condition for reductable according to Frobenius is obtained. By using another method, the same condition is obtained where the existence of the natural number \(n\) is replaced by the existence of an integer \(n\). For the same class of second-order linear differential equations, the case for reductable according to Frobenius which is independent from an exist of a number \(n\) is reviewed. In both cases, formulas of one particular solution and transformation to a system of first-order differential equations are obtained. In end, this theory is supported by examples.

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Published

2021-05-26

Issue

Vol. 45 No. 2 (2021): 45 (LXXI) 2 (2021)

Section

Articles

License

Copyright (c) 2021 Matematichki Bilten

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

[1]
B. Zlatanovska and B. M. Piperevski, “ON THE INTEGRABILITY OF A CLASS OF DIFFERENTIAL EQUATIONS”, Mat. Bilt., vol. 45, no. 2, pp. 85–93, May 2021, doi: 10.37560/matbil21452085z.