Coexistence of Distributional and Rational Solution to Some Linear Ordinary Differential Equations
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Date
2016-03-21
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Addis Ababa University
Abstract
In this paper, we visit a distributional solution of the di erential equation
ty(n)(t) + my(n1)(t) + ty(t) = 0
where m and n are any integers with n 2 and t 2 R using Laplace transform
technique. We nd that the types of Laplace transformable solution in the
space of right-sided expiration depend on the relationship between m and
n. Precisely, we have a distributional solution provided m n; and a weak
solution otherwise.
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Keywords
Coexistence, Distributional, Rational Solution, Some Linear Ordinary Differential, Equations