Abstract: This work represents part of the detailed calculations of the Plenary Talk presented by the corresponding author at the International Conference on Engineering, Economy, Computer Applications for Natural Sciences and Medicine (EEACS 2025) in Lisbon, Portugal. Modified forms of the standard Nield-Kuznetsov functions of the first- and second-kind are introduced in this work in which power series solutions to the inhomogeneous Airy’s equation are investigated. The forms of solutions for the cases of constant and variable forcing functions are expressed in terms of the modified standard Nield-Kuznetsov functions, and graphs illustrating the two linearly independent power series solutions are obtained using a four-term truncated series. These results illustrate the behaviour of the solutions and of the modified Nield-Kuznetsov functions.

Keywords: Airy’s Inhomogeneous Equation, Power Series, Modified Nield-Kuznetsov Functions

Pages: 47-53

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