Linearization of Third-order Ordinary Differential Equations by Generalized Sundman Transformation

Rakkiet  Srisuntorn; Warisa  Nakpim

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Published: Dec 30, 2016

Keywords:

Linearization problem Generalized Sundman transformation Third-order ordinary differential equations

Rakkiet Srisuntorn

Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand

Warisa Nakpim

Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand

Abstract

This research considers an application of the generalized Sundman transformation, i.e.,
$gif.latex?u(t)&space;=&space;f(x,y)$
$gif.latex?dt&space;=&space;g(x,y)dx$
to the linearization problem of third-order ordinary differential equations. Complete necessary and sufficient conditions for third-order ordinary differential equations to be linearizable into the general form of a linear third-order ordinary differential equation
$gif.latex?u'''&space;+&space;\beta&space;u''&space;+&space;\alpha&space;u'&space;=\gamma&space;u&space;=&space;\eta$
where $gif.latex?\beta$ , $gif.latex?\alpha$ , $gif.latex?\gamma$ and $gif.latex?\eta$ are constants, are obtained for the case $gif.latex?f_{x}$ = 0.

How to Cite

Srisuntorn, R. ., & Nakpim, W. . (2016). Linearization of Third-order Ordinary Differential Equations by Generalized Sundman Transformation. KKU Science Journal, 44(4), 705–718. Retrieved from https://ph01.tci-thaijo.org/index.php/KKUSciJ/article/view/249624

Issue

Vol. 44 No. 4 (2016): October - December 2016

Section

Research Articles

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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