Finding Bessel Solutions for a Differential Equation with a Transformed Format

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Homework Help Overview

The discussion revolves around a differential equation of the form u'' - bc(x^m)u = 0, which is a transformed version of a related equation involving a non-homogeneous polynomial term. Participants are exploring how to express the general solution in terms of Bessel functions.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Some participants question the necessity of transforming the original differential equation, suggesting that it may be solvable directly as a constant coefficient differential equation. Others note the importance of correctly identifying the terms in the original equation.

Discussion Status

The discussion is ongoing, with participants sharing their thoughts on the transformation process and its implications. There is a mix of curiosity about the approach taken and the potential for direct solutions, but no consensus has been reached on the best method to proceed.

Contextual Notes

Participants are navigating the complexities of the equation's transformation and its relation to Bessel functions, while also addressing potential typographical errors in the original problem statement.

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Homework Statement


u''-bc (x^m) u =0

Homework Equations


How can I write the general solution in terms of Bessel function?

The Attempt at a Solution



This form is a transformed vresion of y'+by^2=cx^m with dummy variable by=1/u *du/dx
 
Last edited:
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ramtin said:

Homework Statement


u''-bc (x^m) u =0


Homework Equations


How can I write the general solution in terms of Bessel function?


The Attempt at a Solution



This form is a transformed vresion of y'+by=cx^m with dummy variable by=1/u *du/dx

I'm curious why you would go to the trouble of transforming your original DE when you can solve it directly. It's just a constant coefficient DE with a non-homogeneous polynomial term.
 
LCKurtz said:
I'm curious why you would go to the trouble of transforming your original DE when you can solve it directly. It's just a constant coefficient DE with a non-homogeneous polynomial term.

it was y'+by^2=cx^m ,Iforgot to type the y squared power
 
Here is what Maple gives, for what it's worth:

bessel.jpg
 

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