Iman Transform for Solving Linear Ordinary Differential Equations with Variable Coefficients
DOI:
https://doi.org/10.35778/jazu.i56.a674Keywords:
Iman Transform, Linear Ordinary Differential Equations, Variable Coefficients, Integral Transforms, Applied MathematicsAbstract
This manuscript presents a novel integral transform, designated as the Iman transform, which is employed to resolve ordinary differential equations characterized by variable coefficients, owing to their critical significance across diverse domains, particularly within applied mathematics. The Iman transform is categorized as a contemporary integral transform, which has previously exhibited its efficacy in addressing equations with constant coefficients. This investigation elucidates the operational attributes of the transform and accentuates its capacity to convert differential equations with variable coefficients into more manageable forms. In the course of this research, explicit formulations of the Iman transform are established for specific functions , and these formulations are utilized to tackle initial value problems featuring variable coefficients. The results indicate that the Iman transform furnishes a precise and dependable methodology for deriving analytical solutions, obviating the necessity for conventional approaches and highlighting its importance as a formidable instrument in the analysis and resolution of this category of differential equations.
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