Abstract
This research paper aims to identify and also tries to prove differential equation of first order that has Hyers-Ulam and Generalized Hyers-Ulam stability by inducing Fourier Transform method.The analysis of the Hyers-Ulam stability had resulted in providing a constant value for homogeneous and non-homogeneous differential equation with implementation of Fourier transform. In order to prove these facts, few application of non-homogeneous linear differential equation in connect with the main results are provided.
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