λ–SYMMETRIES ON THE DERIVATION OF FIRST INTEGRALS OF ORDINARY DIFFERENTIAL EQUATIONS

2010 ◽  
Author(s):  
C. MURIEL ◽  
J. L. ROMERO
Keyword(s):  
Differential Equations ◽  
Ordinary 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.

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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