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

Amornrat Sangsuwan, Kamsing Nonlaopon, Somsak Orankitjaroen and Ismail Mirumbe
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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

Mathematics, 2019, vol. 7, issue 10, 1-8

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.

Keywords: Cauchy–Euler equations; distributional solution; Dirac delta function; generalized solution; Laplace transform (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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