k-Hypergeometric Series Solutions to One Type of Non-Homogeneous k-Hypergeometric Equations

In this paper, we expound on the hypergeometric series solutions for the second-order non-homogeneous k-hypergeometric differential equation with the polynomial term. The general solutions of this equation are obtained in the form of k-hypergeometric series based on the Frobenius method. Lastly, we employ the result of the theorem to find the solutions of several non-homogeneous k-hypergeometric differential equations.

Download Full-text

Solutions ofk-Hypergeometric Differential Equations

Journal of Applied Mathematics ◽

10.1155/2014/128787 ◽

2014 ◽

Vol 2014 ◽

pp. 1-13 ◽

Cited By ~ 3

Author(s):

Shahid Mubeen ◽

Mammona Naz ◽

Abdur Rehman ◽

Gauhar Rahman

Keyword(s):

Differential Equation ◽

Differential Equations ◽

Linear Differential Equation ◽

Second Order ◽

Order Linear Differential Equation ◽

Frobenius Method ◽

Order Linear ◽

Hypergeometric Differential Equation ◽

Linear Differential

We solve the second-order linear differential equation called thek-hypergeometric differential equation by using Frobenius method around all its regular singularities. At each singularity, we find 8 solutions corresponding to the different cases for parameters and modified our solutions accordingly.

Download Full-text

A mechanical method for the solution of second-order linear differential equations

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004100009804 ◽

1931 ◽

Vol 27 (4) ◽

pp. 546-552 ◽

Cited By ~ 1

Author(s):

E. C. Bullard ◽

P. B. Moon

Keyword(s):

Differential Equation ◽

Differential Equations ◽

Boundary Conditions ◽

Order Differential Equation ◽

Second Order ◽

Linear Differential Equations ◽

Mechanical Method ◽

Order Linear ◽

Second Order Differential Equation ◽

Linear Differential

A mechanical method of integrating a second-order differential equation, with any boundary conditions, is described and its applications are discussed.

Download Full-text

Periodic solutions for periodic second-order differential equations with variable potentials

Journal of Applied Analysis ◽

10.1515/jaa-2018-0013 ◽

2018 ◽

Vol 24 (2) ◽

pp. 127-137

Author(s):

Jaume Llibre ◽

Ammar Makhlouf

Keyword(s):

Differential Equation ◽

Differential Equations ◽

Periodic Solutions ◽

Order Differential Equation ◽

Sufficient Conditions ◽

Second Order ◽

Second Order Differential Equations ◽

Second Order Differential Equation ◽

Existence Of Periodic Solutions

Abstract We provide sufficient conditions for the existence of periodic solutions of the second-order differential equation with variable potentials {-(px^{\prime})^{\prime}(t)-r(t)p(t)x^{\prime}(t)+q(t)x(t)=f(t,x(t))} , where the functions {p(t)>0} , {q(t)} , {r(t)} and {f(t,x)} are {\mathcal{C}^{2}} and T-periodic in the variable t.

Download Full-text

On the Existence of Eigenmodes of Linear Quasi-Periodic Differential Equations and their Relation to the MHD Continuum

Zeitschrift für Naturforschung A ◽

10.1515/zna-1982-0816 ◽

1982 ◽

Vol 37 (8) ◽

pp. 830-839 ◽

Cited By ~ 1

Author(s):

A. Salat

Keyword(s):

Differential Equation ◽

Ordinary Differential Equation ◽

Differential Equations ◽

Infinite Sequence ◽

Periodic Coefficient ◽

Second Order ◽

Order Ordinary Differential Equation ◽

Magnetic Surfaces ◽

Toroidal Geometry

The existence of quasi-periodic eigensolutions of a linear second order ordinary differential equation with quasi-periodic coefficient f{ω1t, ω2t) is investigated numerically and graphically. For sufficiently incommensurate frequencies ω1, ω2, a doubly indexed infinite sequence of eigenvalues and eigenmodes is obtained.The equation considered is a model for the magneto-hydrodynamic “continuum” in general toroidal geometry. The result suggests that continuum modes exist at least on sufficiently ir-rational magnetic surfaces

Download Full-text

Oscillation Criteria for Second Order Neutral Differential Equations

Canadian Journal of Mathematics ◽

10.4153/cjm-1996-044-6 ◽

1996 ◽

Vol 48 (4) ◽

pp. 871-886 ◽

Cited By ~ 14

Author(s):

Horng-Jaan Li ◽

Wei-Ling Liu

Keyword(s):

Differential Equation ◽

Differential Equations ◽

Delay Differential Equations ◽

Second Order ◽

Neutral Delay ◽

Oscillation Criteria ◽

Neutral Differential Equations ◽

Neutral Delay Differential Equation ◽

Image Position ◽

Delay Differential

AbstractSome oscillation criteria are given for the second order neutral delay differential equationwhere τ and σ are nonnegative constants, . These results generalize and improve some known results about both neutral and delay differential equations.

Download Full-text

Solutions of the perturbed KdV equation for convecting fluids by factorizations

Open Physics ◽

10.2478/s11534-009-0116-7 ◽

2010 ◽

Vol 8 (4) ◽

Cited By ~ 2

Author(s):

Octavio Cornejo-Pérez ◽

Haret Rosu

Keyword(s):

Differential Equation ◽

Differential Equations ◽

Order Differential Equation ◽

Kdv Equation ◽

Travelling Wave ◽

Second Order ◽

Travelling Wave Solutions ◽

Second Order Differential Equation ◽

Wave Solutions ◽

Perturbed Kdv Equation

AbstractIn this paper, we obtain some new explicit travelling wave solutions of the perturbed KdV equation through recent factorization techniques that can be performed when the coefficients of the equation fulfill a certain condition. The solutions are obtained by using a two-step factorization procedure through which the perturbed KdV equation is reduced to a nonlinear second order differential equation, and to some Bernoulli and Abel type differential equations whose solutions are expressed in terms of the exponential andWeierstrass functions.

Download Full-text

Interval oscillation criteria for certain forced second-order differential equations

Carpathian Journal of Mathematics ◽

10.37193/cjm.2012.02.01 ◽

2012 ◽

Vol 28 (2) ◽

pp. 337-344

Author(s):

ERCAN TUNC ◽

Keyword(s):

Differential Equation ◽

Differential Equations ◽

Second Order ◽

Half Line ◽

Oscillation Criteria ◽

Second Order Differential Equations ◽

Interval Oscillation

By using generalized Riccati transformations and an inequality due to Hardy et al., several new interval oscillation criteria are established for the nonlinear damped differential equation... The new interval oscillation criteria are different from most known ones in the sense they are based on the information only on a sequence of subintervals of [t0, ∞), rather than on the whole half-line. Our results improve and extend the known some results in the literature.

Download Full-text

XIII.—Partial Differential Equations and the Calculus of Variations

Proceedings of the Royal Society of Edinburgh ◽

10.1017/s0370164600021957 ◽

1927 ◽

Vol 46 ◽

pp. 126-135 ◽

Cited By ~ 1

Author(s):

E. T. Copson

Keyword(s):

Differential Equation ◽

Partial Differential Equation ◽

Partial Differential Equations ◽

Differential Equations ◽

Calculus Of Variations ◽

Order Equation ◽

Second Order ◽

Physical Problem ◽

Partial Differential ◽

Hamiltonian Principle

A partial differential equation of physics may be defined as a linear second-order equation which is derivable from a Hamiltonian Principle by means of the methods of the Calculus of Variations. This principle states that the actual course of events in a physical problem is such that it gives to a certain integral a stationary value.

Download Full-text