Some Approaches for Solving Multiplicative Second-Order Linear Differential Equations with Variable Exponentials and Multiplicative Airy’s Equation

Abstract

This paper offers several approaches for solving multiplicative second-order linear differential equations with variable exponentials, such as normalization and reduction to Riccati equations. In addition, in this paper, the multiplicative version of the Airy equation, which emerges in fluid mechanics, geophysics, and atomic physics, is solved using the multiplicative power series solution method.

Keywords

• Multiplicative calculus
• transformation
• Airy’s equation

İkinci Mertebeden Değişken Üslü Çarpımsal Lineer Diferansiyel Denklemlerin ve Çarpımsal Airy Denkleminin Çözümleri için Bazı Yaklaşımlar

Abstract

Bu makale, normalleşme ve Riccati denklemlerine indirgenme gibi ikinci mertebeden değişken katsayılı çarpımsal lineer diferansiyel denklemleri çözmek için çeşitli yaklaşımlar sunmaktadır. Ayrıca bu makalede akışkan mekaniği, jeofizik ve atom fiziğinde ortaya çıkan Airy denkleminin çarpımsal versiyonu çarpımsal kuvvet serisi çözüm yöntemi kullanılarak çözülmüştür.

Keywords

• Çarpımsal hesap
• dönüşüm
• çarpımsal Airy denklemi

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