Differential equations with a given set of solutions

Jaume Llibre, Rafael Ramírez and Natalia Sadovskaia

Applied Mathematics and Computation, 2020, vol. 365, issue C

Abstract: The aim of this paper is to study the following inverse problem of ordinary differential equations: For a given set of analytic functions ω={z1(t),…,zr(t)}, with zj(t)=xj(t)+iyj(t) and z¯j(t)=xj(t)−iyj(t) for j=1,…,r, defined in the open interval I⊆R, we want to determine the differential equationF(t,z¯,z,z˙,z¯˙,…,z(n),z¯(n))=0,where z(j)=djzdtj for j=1,…,n, in such a way that the given set of functions ω is a set of solutions of this differential equation.

Keywords: Planar differential system; Inverse problem for ordinary differential equations; Ricatti equation; Abel equation; First integral (search for similar items in EconPapers)
Date: 2020
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300319306514
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:365:y:2020:i:c:s0096300319306514

DOI: 10.1016/j.amc.2019.124659

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().