On the Solution Space of Ordinary Differential Equations With Polynomial Coefficients

Opio, I.; Mirumbe, G. I.; Ssebuliba, J.; Mango, John Magero

doi:10.17654/ms101010103

Cited by 2 publications

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“…Thus, we have the repeated real roots of (22), that is r = m. Therefore, the solution of (20) is Y(s) = s m . Now, Y(s) is an analytic function over the entire s-plane.…”

Section: Theoremmentioning

confidence: 99%

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Generalized Solutions of the Third-Order Cauchy-Euler Equation in the Space of Right-Sided Distributions via Laplace Transform

2019

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Using the Laplace transform technique, we investigate the generalized solutions of the third-order Cauchy-Euler equation of the form t 3 y ′ ′ ′ ( t ) + a t 2 y ′ ′ ( t ) + b y ′ ( t ) + c y ( t ) = 0 , where a , b , and c ∈ Z and t ∈ R . We find that the types of solutions in the space of right-sided distributions, either distributional solutions or weak solutions, depend on the values of a, b, and c. At the end of the paper, we give some examples showing the types of solutions. Our work improves the result of Kananthai (Distribution solutions of the third order Euler equation. Southeast Asian Bull. Math. 1999, 23, 627–631).

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“…Thus, we have the repeated real roots of (22), that is r = m. Therefore, the solution of (20) is Y(s) = s m . Now, Y(s) is an analytic function over the entire s-plane.…”

Section: Theoremmentioning

confidence: 99%

“…where m, n ∈ Z with n ≥ 2 and t ∈ R. Opio et al [22] studied those of the differential equation with polynomial coefficients of the form…”

Section: Introductionmentioning

confidence: 99%

Generalized Solutions of the Third-Order Cauchy-Euler Equation in the Space of Right-Sided Distributions via Laplace Transform

2019

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“…where , ∈ , 2, ∈ . Opio et al [18] studied those of the differential equation with polynomial coefficients of the form.…”

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confidence: 99%

On Distributional Solutions of a Singular Differential Equation of 2-order in the Space K’

Abdourahman¹

2022

IJTAM

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The main purpose of this work is to describe all the zero-centered solutions of the second order linear singular differential equation with Dirac delta function (or it derivatives of some order) in the second right hand side in the space K'. All the coefficients and the exponents of the polynomials under the unknown function and it derivatives up to second order respectively, are real and natural numbers in the considered equation. We conduct investigations for both the euler case and left euler case situations of this equation, when it is fulfilled some particular conditions in the relationships between the parameters A, B, C, m, n and r. In each of these cases, we look for the zero-centered solutions and substitute the form of the particular solution into the equation. We then after, determinate the unknown coefficients and formulate the related theorems to describe all the solutions depending of the cases to be investigated.

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On the Solution Space of Ordinary Differential Equations With Polynomial Coefficients

Cited by 2 publications

References 0 publications

Generalized Solutions of the Third-Order Cauchy-Euler Equation in the Space of Right-Sided Distributions via Laplace Transform

Generalized Solutions of the Third-Order Cauchy-Euler Equation in the Space of Right-Sided Distributions via Laplace Transform

On Distributional Solutions of a Singular Differential Equation of 2-order in the Space K’

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