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Series solution near an ordinary point

  1. Oct 4, 2006 #1
    some help with series solutions

    I'm needing help on series solutions. It's been a while since I worked on them.

    Find
    [tex]\phi''(x_{0})[/tex]
    [tex]\phi'''(x_{0})[/tex]
    [tex]\phi''''(x_{0})[/tex]


    y"+xy'+y=0; y(0)=1. y'(0)=0
     
    Last edited: Oct 4, 2006
  2. jcsd
  3. Oct 5, 2006 #2

    Pyrrhus

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    Homework Helper

    is [itex] \phi (x) [/itex] a solution of the initial value problem?

    if it its then start with

    [tex] \phi '' (x) + x \phi ' (x) +\phi (x) = 0 [/tex]
     
  4. Oct 5, 2006 #3

    HallsofIvy

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    and
    [tex]\phi'''(x)+ x\phi''(x)+ \phi'(x)= 0[/tex]
    [tex]\phi''''(x)+ x\phi'''(x)+ \phi''(x)= 0[/tex]
     
  5. Oct 8, 2006 #4
    I have a question that involves using those derivatives. It's asks to determine the values at those derivatives with y(0)=1, y'(0)=1

    When I used those numbers I didn't get the correct answer, which is -1, 0, 3. I think the derivatives are wrong.
     
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