Bessel's equation and laplace transform

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Discussion Overview

The discussion revolves around Bessel's equation of order zero and its relationship with the Laplace transform. Participants are exploring the mathematical properties and transformations related to the differential equation, particularly in the context of solving it without initial boundary values.

Discussion Character

  • Homework-related

Main Points Raised

  • One participant presents Bessel's equation of order zero and seeks to show that the Laplace transform of its finite solution at the origin, denoted as J[SIZE="1"]0, is proportional to (s^2+1)^-1/2.
  • Another participant asks for the Laplace transform of the differential equation.
  • A different participant expresses difficulty in finding the Laplace transform due to the absence of initial boundary values.
  • One participant requests assistance with the problem.

Areas of Agreement / Disagreement

There is no consensus on how to proceed with the problem, as participants express different challenges and uncertainties regarding the Laplace transform and the lack of initial boundary conditions.

samdawy
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Homework Statement


Bessel's equation of order zero can be written

xy''+y'+xy=0

Homework Equations



Denote the solution which is finite a the origin by J0 Show that the Laplace transform of J0 is proportional to (s^2+1)^-1/2


The Attempt at a Solution

 
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What's the laplace transform of that DE?
 
I can't find the laplace because there are no initial boundary values
 
anyone can help me?
 

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