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The Generalized Solutions of the n th Order Cauchy–Euler Equation

Author

Listed:
  • Amornrat Sangsuwan

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

  • Kamsing Nonlaopon

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

  • Somsak Orankitjaroen

    (Department of Mathematics, Faculty of Science, Mahidol University, Bangkok 10400, Thailand)

  • Ismail Mirumbe

    (Department of Mathematics, Makerere University, Kampala 7062, Uganda)

Abstract

In this paper, we use the Laplace transform technique to examine the generalized solutions of the n th order Cauchy–Euler equations. By interpreting the equations in a distributional way, we found that whether their solution types are classical, weak or distributional solutions relies on the conditions of their coefficients. To illustrate our findings, some examples are exhibited.

Suggested Citation

  • Amornrat Sangsuwan & Kamsing Nonlaopon & Somsak Orankitjaroen & Ismail Mirumbe, 2019. "The Generalized Solutions of the n th Order Cauchy–Euler Equation," Mathematics, MDPI, vol. 7(10), pages 1-8, October.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:10:p:932-:d:274747
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    References listed on IDEAS

    as
    1. S. M. Shah & Joseph Wiener, 1983. "Distributional and entire solutions of ordinary differential and functional differential equations," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 6, pages 1-27, January.
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    Cited by:

    1. Waritsara Thongthai & Kamsing Nonlaopon & Somsak Orankitjaroen & Chenkuan Li, 2023. "Generalized Solutions of Ordinary Differential Equations Related to the Chebyshev Polynomial of the Second Kind," Mathematics, MDPI, vol. 11(7), pages 1-14, April.

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