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Generation and Identification of Ordinary Differential Equations of Maximal Symmetry Algebra

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  • J. C. Ndogmo

Abstract

An effective method for generating linear ordinary differential equations of maximal symmetry in their most general form is found, and an explicit expression for the point transformation reducing the equation to its canonical form is obtained. New expressions for the general solution are also found, as well as several identification and other results and a direct proof of the fact that a linear ordinary differential equation is iterative if and only if it is reducible to the canonical form by a point transformation. New classes of solvable equations parameterized by an arbitrary function are also found, together with simple algebraic expressions for the corresponding general solution.

Suggested Citation

  • J. C. Ndogmo, 2016. "Generation and Identification of Ordinary Differential Equations of Maximal Symmetry Algebra," Abstract and Applied Analysis, John Wiley & Sons, vol. 2016(1).
    • Handle: RePEc:wly:jnlaaa:v:2016:y:2016:i:1:n:1796316
    DOI: 10.1155/2016/1796316
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    References listed on IDEAS

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    1. K. S. Mahomed & E. Momoniat, 2012. "Symmetry Classification of First Integrals for Scalar Linearizable Second‐Order ODEs," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    2. J. C. Ndogmo, 2012. "Some Results on Equivalence Groups," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    3. J. C. Ndogmo, 2012. "Some Results on Equivalence Groups," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-11, October.
    4. K. S. Mahomed & E. Momoniat, 2012. "Symmetry Classification of First Integrals for Scalar Linearizable Second-Order ODEs," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-14, November.
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    1. J. C. Ndogmo, 2017. "First Integrals and Hamiltonians of Some Classes of ODEs of Maximal Symmetry," Journal of Applied Mathematics, John Wiley & Sons, vol. 2017(1).

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