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Bessel+starting part?

  1. Jul 16, 2009 #1
    this is my final exam question, I can't figure how to start
    thx for your help


    " Obtain the solution of the following differential equation in the form of bessel equation;

    [tex]x^2\frac{d^2 y}{dx^2} + \frac{1}{8}{x}\frac{dy}{dx} + (k^4x^8-6)y=0[/tex] "
     
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  3. Jul 16, 2009 #2

    George Jones

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    Is this question from a take-home exam, or is it a question that you couldn't do from an exam that you have already submitted?
     
  4. Jul 17, 2009 #3
    yes I couldn't do this in exam, I try it in two way


    * [tex] y= \sum_{n=\zero}^\infty C_nx^{(n+r)}}[/tex] from this I found [tex] \frac {dy}{dx} and \frac {d^2y}{dx^2}[/tex] and put them to equection and go on with frobenius method but I couldn't find "r" becouse of too many indicial equations so I couldn't find the method to recurrance equation and go on...


    *I try to make the equation similar to [tex]x^2\frac{d^2 y}{dx^2} + {x}\frac{dy}{dx} + (\beta x^2 - n^2)y=0[/tex] so then I could write [tex]y(x) = AJ_{n}(\beta x) + BY_{n}(\beta x) [/tex] is the solution;

    I try to put [tex]y=x^\alpha t [/tex] also [tex]t=x^\alpha with \frac {dy}{dx}=\frac {dy}{dt}*\frac{dt}{dx}[/tex] ,but couldn'tmake it similar

    can you give me a way to strat
     
    Last edited: Jul 17, 2009
  5. Jul 17, 2009 #4
    Hi there,

    have a look at the pdf, it might help

    All the Best

    Muzialis
     

    Attached Files:

  6. Jul 31, 2009 #5
    I found some example questions with reducing equations and answers, also find my problem's reducing equations;(from KREYSZIG -advanced engineering mathematics)
    thx

    http://img41.imageshack.us/img41/43/exampless.jpg [Broken]
     
    Last edited by a moderator: May 4, 2017
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