Differential Equations with Given Partial and First Integrals

2016 ◽  
pp. 1-40
Author(s):  
Jaume Llibre ◽  
Rafael Ramírez
Keyword(s):  
Differential Equations ◽  
First Integrals

On Integrating Factors and a Perturbation Method

1995 ◽  
Author(s):  
W. T. van Horssen
Keyword(s):  
Differential Equations ◽  
Perturbation Method ◽  
Ordinary Differential Equations ◽  
First Integrals ◽  
Van Der Pol Equation ◽  
Van Der Pol ◽  
Order Ordinary Differential Equation ◽  
First Order ◽  
Integrating Factors ◽  
Complete Solutions

Abstract In this paper the fundamental concept (due to Euler, 1734) of how to make a first order ordinary differential equation exact by means of integrating factors, is extended to n-th order (n ≥ 2) ordinary differential equations and to systems of first order ordinary differential equations. For new classes of differential equations first integrals or complete solutions can be constructed. Also a perturbation method based on integrating factors can be developed. To show how this perturbation method works the method is applied to the well-known Van der Pol equation.

scholarly journals Lax Pairs and First Integrals for Autonomous and Non-Autonomous Differential Equations Belonging to the Painlevé – Gambier List

2020 ◽  
Vol 16 (4) ◽  
pp. 637-650
Author(s):  
P. Guha ◽  
◽  
S. Garai ◽  
A.G. Choudhury ◽  
◽  
...  
Keyword(s):  
Differential Equations ◽  
First Integral ◽  
Lax Pair ◽  
First Integrals ◽  
Second Order ◽  
Lax Representation ◽  
Lax Pairs ◽  
Second Order Differential Equations ◽  
Autonomous Version ◽  
Autonomous Differential Equations

Recently Sinelshchikov et al. [1] formulated a Lax representation for a family of nonautonomous second-order differential equations. In this paper we extend their result and obtain the Lax pair and the associated first integral of a non-autonomous version of the Levinson – Smith equation. In addition, we have obtained Lax pairs and first integrals for several equations of the Painlevé – Gambier list, namely, the autonomous equations numbered XII, XVII, XVIII, XIX, XXI, XXII, XXIII, XXIX, XXXII, XXXVII, XLI, XLIII, as well as the non-autonomous equations Nos. XV and XVI in Ince’s book.

Liouvillian first integrals of differential equations

2011 ◽  
Vol 94 ◽  
pp. 153-161 ◽  
Author(s):  
Guy Casale
Keyword(s):  
Differential Equations ◽  
First Integrals

On first integrals of second-order ordinary differential equations

2013 ◽  
Vol 82 (1) ◽  
pp. 17-30 ◽  
Author(s):  
S. V. Meleshko ◽  
S. Moyo ◽  
C. Muriel ◽  
J. L. Romero ◽  
P. Guha ◽  
...  
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
First Integrals ◽  
Second Order

On the polynomial first integrals of certain second‐order differential equations

1982 ◽  
Vol 23 (12) ◽  
pp. 2281-2285 ◽  
Author(s):  
F. G. Gascón ◽  
F. B. Ramos ◽  
E. Aguirre‐Daban
Keyword(s):  
Differential Equations ◽  
First Integrals ◽  
Second Order ◽  
Second Order Differential Equations

First Integrals of a Cubic System of Differential Equations

2008 ◽  
Author(s):  
Zhibek Kadyrsizova ◽  
Valery G. Romanovski ◽  
Marko Robnik ◽  
Valery Romanovski
Keyword(s):  
Differential Equations ◽  
First Integrals ◽  
System Of Differential Equations ◽  
Cubic System
Sign in / Sign up

Export Citation Format

Share Document