Bessel's ordinary differential equation and Bessel functions are likely to occur in problems showing cylindrical symmetry, and these carries weight in electric fields, heat equation, vibrations and so on. It is well known fact that a general solution of Bessel's equation should be expressed by Bessel function, and it consists of intricate forms. In this article, we have proposed the solution of Bessel's equation by using integral transforms, and surely, this is simpler than established method.
Abstract:The subjects on the solution of differential equations with variable coefficients have aroused the interest of many researchers. Existing many integral transforms are playing a role to get the solution of it. In this sense, we have researched about several forms of Euler-Cauchy equation, using Laplace transform. Related to the topic, the proposed idea can be also applied to other transforms (Sumudu/Elzaki, etc.).
We have showed that the Laplace transform of derivative can be expressed by an infinite series or Heaviside function. Related to this topic, the proposed idea can be also applied to other transforms(Sumudu/Elzaki).
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