On the Derivation of a Closed-Form Expression for the Solutions of a Subclass of Generalized Abel Differential Equations
Joint Authors
Tsiakalos, Apostolos
Nastou, Panayotis E.
Stamatiou, Yannis C.
Spirakis, Paul
Source
International Journal of Differential Equations
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-9, 9 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-07-08
Country of Publication
Egypt
No. of Pages
9
Main Subjects
Abstract EN
We investigate the properties of a general class of differential equations described by dy(t)/dt=fk+1(t)y(t)k+1+fk(t)y(t)k+⋯+f2(t)y(t)2+f1(t)y(t)+f0(t), with k>1 a positive integer and fi(t), 0≤i≤k+1, with fi(t), real functions of t.
For k=2, these equations reduce to the class of Abel differential equations of the first kind, for which a standard solution procedure is available.
However, for k>2 no general solution methodology exists, to the best of our knowledge, that can lead to their solution.
We develop a general solution methodology that for odd values of k connects the closed form solution of the differential equations with the existence of closed-form expressions for the roots of the polynomial that appears on the right-hand side of the differential equation.
Moreover, the closed-form expression (when it exists) for the polynomial roots enables the expression of the solution of the differential equation in closed form, based on the class of Hyper-Lambert functions.
However, for certain even values of k, we prove that such closed form does not exist in general, and consequently there is no closed-form expression for the solution of the differential equation through this methodology.
American Psychological Association (APA)
Nastou, Panayotis E.& Spirakis, Paul& Stamatiou, Yannis C.& Tsiakalos, Apostolos. 2013. On the Derivation of a Closed-Form Expression for the Solutions of a Subclass of Generalized Abel Differential Equations. International Journal of Differential Equations،Vol. 2013, no. 2013, pp.1-9.
https://search.emarefa.net/detail/BIM-508973
Modern Language Association (MLA)
Nastou, Panayotis E.…[et al.]. On the Derivation of a Closed-Form Expression for the Solutions of a Subclass of Generalized Abel Differential Equations. International Journal of Differential Equations No. 2013 (2013), pp.1-9.
https://search.emarefa.net/detail/BIM-508973
American Medical Association (AMA)
Nastou, Panayotis E.& Spirakis, Paul& Stamatiou, Yannis C.& Tsiakalos, Apostolos. On the Derivation of a Closed-Form Expression for the Solutions of a Subclass of Generalized Abel Differential Equations. International Journal of Differential Equations. 2013. Vol. 2013, no. 2013, pp.1-9.
https://search.emarefa.net/detail/BIM-508973
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-508973