On the Ni(x) integral function and its application to the Airy’s non-homogeneous equation

On The Nield-Koznetsov Integral Function and Its Application to Airy’s Inhomogeneous Boundary Value Problem

“…General solution to ODE (1) is the sum of the complementary function, given by equation (4) as the solution to the homogeneous Airy's ODE, and the particular solution, , which, using variation of parameters, is assumed to be of the form … (11) where the functions and are given by the following forms, respectively, with the help of (7):…”

“…Rooted in Airy's nineteenth century work in optics, Airy's ODE continues to receive interest due to the reduction of many differential equations in mathematical physics to it by an appropriate change of variables (cf. [4,5,8,11,12] and the references therein).…”

A Note on Taylor Series Representation of the Nield-Kuznetsov Function of the Second Kind

“…where 𝑅 ∈ ℜ. Hamdan and Kamel, [3], showed that the general solution to (1) is expressible in the form:…”

Flow through a Variable Permeability Brinkman Porous Core

“…A main objective of this undertaking is to study the effects of thin porous Darcy layers on the variable permeability flow in a Brinkman layer. In order to accomplish this work, we choose a Brinkman permeability function that reduces Brinkman's equation to the well-known inhomogeneous Airy's differential equation [15]. We provide an analytical solution to the resulting Airy's inhomogeneous equation, and we provide computations using Maple's built-in functions to evaluate Airy's functions.…”