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On first integrals of second-order ordinary differential equations

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Abstract

Here we discuss first integrals of a particular representation associated with second-order ordinary differential equations. The linearization problem is a particular case of the equivalence problem together with a number of related problems such as defining a class of transformations, finding invariants of these transformations, obtaining the equivalence criteria, and constructing the transformation. The relationship between the integral form, the associated equations, equivalence transformations, and some examples are considered as part of the discussion illustrating some important aspects and properties.

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Authors and Affiliations

  1. School of Mathematics, Suranaree University of Technology, Nakhon Ratchasima, 30000, Thailand

    S. V. Meleshko

  2. Department of Mathematics, Statistics and Physics, Institute for Systems Science, Durban University of Technology, P O Box 1334, Steve Biko Campus, Durban, 4000, South Africa

    S. Moyo

  3. Departamento de Matemáticas, Universitario de Puerto Real, 11510, Puerto Real, Cádiz, Spain

    C. Muriel & J. L. Romero

  4. S.N. Bose National Centre for Basic Sciences, J D Block, Sector III, Salt Lake, Calcutta, 700098, West Bengal, India

    P. Guha

  5. Department of Physics, Surendranath College, 24/2 Mahatma Gandhi Road, Calcutta, 700009, West Bengal, India

    A. G. Choudhury

Authors
  1. S. V. Meleshko
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  2. S. Moyo
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  3. C. Muriel
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  4. J. L. Romero
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  5. P. Guha
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  6. A. G. Choudhury
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Corresponding author

Correspondence to S. Moyo.

Additional information

To Professor Peter Leach on his seventieth birthday.

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Meleshko, S.V., Moyo, S., Muriel, C. et al. On first integrals of second-order ordinary differential equations. J Eng Math 82, 17–30 (2013). https://doi.org/10.1007/s10665-012-9590-9

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  • DOI: https://doi.org/10.1007/s10665-012-9590-9

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