The New Integral Transform ''Aboodh Transform
khalid suliman
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Abstract
In this paper a new integral transform namely Aboodh transform was applied to solve linear ordinary differential equations with constant coefficients.
Key takeaways
- Typically, Fourier, Laplace, ELzaki and Sumudu transforms are the convenient mathematical tools for solving differential equations, Also Aboodh transform and some of its fundamental properties are used to solve differential equations.
- A new transform called the Aboodh transform defined for function of exponential order we consider functions in the set A defined by
- The Sufficient Conditions for the existence of Aboodh transform are that ( ) f t for 0 t be piecewise continuous and of exponential order, Otherwise Aboodh transform may or may not exist.
- The following examples illustrate the use of the Aboodh transform in solving certain initial value problems described by ordinary differential equations.
- The inverse Aboodh transform of this equation is simply obtained as ( ) cos sin y x x x Example (4) Consider the second-order differential equation
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