Mathematics (Oct 2019)

The Generalized Solutions of the <i>n</i>th Order Cauchy–Euler Equation

  • Amornrat Sangsuwan,
  • Kamsing Nonlaopon,
  • Somsak Orankitjaroen,
  • Ismail Mirumbe

DOI
https://doi.org/10.3390/math7100932
Journal volume & issue
Vol. 7, no. 10
p. 932

Abstract

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In this paper, we use the Laplace transform technique to examine the generalized solutions of the nth 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.

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