Ordinary differential equations invariant under translation in the independent variable and rescaling: The Lagrangian formulation |
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| Authors: | S Moyo |
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| Institution: | a Department of Mathematics and Centre For Systems Research, Durban Institute of Technology, PO Box 953, Berea Campus, Durban 4000, South Africa
b School of Mathematical Sciences, Howard College Campus, University of KwaZulu-Natal, Durban 4041, South Africa |
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| Abstract: | The Lagrangian formulation of the class of general second-order ordinary differential equations invariant under translation in the independent variable and rescaling is presented. The differential equations arising from this analysis are analysed using the Painlevé test. The well-known differential equation, y″+yy′+ky3=0, is a unique member of this class when k=3 since it is linearisable by a point transformation. A wider subset is shown to be linearisable by means of a nonlocal transformation. |
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