Algebraic properties of first integrals for systems of second-order ordinary differential equations of maximal symmetry

2016 ◽  
Vol 39 (6) ◽  
pp. 715-726
Author(s):  
A. Aslam ◽  
K.S. Mahomed ◽  
E. Momoniat
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
First Integrals ◽  
Second Order ◽  
Maximal Symmetry ◽  
Algebraic Properties

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

scholarly journals Exact Solutions for Certain Nonlinear Autonomous Ordinary Differential Equations of the Second Order and Families of Two-Dimensional Autonomous Systems

2010 ◽  
Vol 2010 ◽  
pp. 1-13 ◽  
Author(s):  
M. P. Markakis
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Autonomous Systems ◽  
Closed Form Solution ◽  
First Integrals ◽  
Form Solution ◽  
Second Order ◽  
Two Dimensional ◽  
First Order ◽  
Abel Equations

Certain nonlinear autonomous ordinary differential equations of the second order are reduced to Abel equations of the first kind ((Ab-1) equations). Based on the results of a previous work, concerning a closed-form solution of a general (Ab-1) equation, and introducing an arbitrary function, exact one-parameter families of solutions are derived for the original autonomous equations, for the most of which only first integrals (in closed or parametric form) have been obtained so far. Two-dimensional autonomous systems of differential equations of the first order, equivalent to the considered herein autonomous forms, are constructed and solved by means of the developed analysis.

FIRST INTEGRALS OF FIN EQUATIONS FOR STRAIGHT FINS

2009 ◽  
Vol 23 (30) ◽  
pp. 3659-3666 ◽  
Author(s):  
E. MOMONIAT ◽  
C. HARLEY ◽  
T. HAYAT
Keyword(s):  
Temperature Distribution ◽  
Temperature Gradient ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Ordinary Differential Equations ◽  
First Integrals ◽  
Second Order ◽  
Nonlinear Ordinary Differential Equations

First integrals admitted by second-order nonlinear ordinary differential equations modeling the temperature distribution in a straight fin are obtained. After imposing the boundary conditions these first integrals give a relationship between temperature at the fin tip and the temperature gradient at the base of the fin in terms of the fin parameters. These first integrals are plotted and analyzed. The results obtained show how the temperature at the fin tip can be controlled by the temperature gradient at the base for fixed fin parameters.

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