Integrating factors and first integrals for ordinary differential equations

1998 ◽  
Vol 9 (3) ◽  
pp. 245-259 ◽  
Author(s):  
STEPHEN C. ANCO ◽  
GEORGE BLUMAN
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
First Integrals ◽  
Integrating Factors

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 On the complete integrability and linearization of certain second-order nonlinear ordinary differential equations

2005 ◽  
Vol 461 (2060) ◽  
pp. 2451-2477 ◽  
Author(s):  
V.K Chandrasekar ◽  
M Senthilvelan ◽  
M Lakshmanan
Keyword(s):  
General Solution ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Free Particle ◽  
First Integrals ◽  
Second Order ◽  
Complete Integrability ◽  
Nonlinear Ordinary Differential Equations ◽  
Integrals Of Motion ◽  
Integrating Factors

A method for finding general solutions of second-order nonlinear ordinary differential equations by extending the Prelle–Singer (PS) method is briefly discussed. We explore integrating factors, integrals of motion and the general solution associated with several dynamical systems discussed in the current literature by employing our modifications and extensions of the PS method. We also introduce a novel way of deriving linearizing transformations from the first integrals to linearize the second-order nonlinear ordinary differential equations to free particle equations. We illustrate the theory with several potentially important examples and show that our procedure is widely applicable.

Erratum: Integrating factors and first integrals for ordinary differential equations

1999 ◽  
Vol 10 (2) ◽  
pp. 223-223
Author(s):  
S. C. ANCO ◽  
G. BLUMAN
Keyword(s):  
Linear System ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
First Integrals ◽  
Integrating Factors ◽  
Linear Pdes

Volume 9 (1998), pp. 245–259The last sentence of §3.2 should read as follows:For n=4, the splitting yields six such linear PDEs from the coefficients of the terms involving Y(6), Y(4), Y(5), Y(5), Y(4)3, Y(4)2 and Y(4).In the first paragraph of §6, the penultimate sentence should read as follows:For an nth-order scalar ODE the determining equations are a linear system of PDEs consisting of the adjoint of the determining equation for symmetries of the nth-order ODE and additional equations when n[ges ]2.We apologise for the errors in the above paper and hope that no inconvenience has been caused to readers.

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
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