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Euler Equation -- diff. equations hw

  1. Jul 30, 2016 #1
    1. The problem statement, all variables and given/known data

    Consider the differential equation (t-2)2y"-2(t-2)y'+2y=0, t>2

    Find r+,r-roots of the indicial polynomial of the equation above.

    2. Relevant equations

    Screen_Shot_2016_07_30_at_2_16_21_PM.png

    3. The attempt at a solution

    y'-[2/(t-2)]y'+[2/(t-2)^2]y=0

    but then I am confused on how to set p(r), what do I do with the t in my a1 and a0


    thanks in advance :)
     
  2. jcsd
  3. Jul 30, 2016 #2

    LCKurtz

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    I think that if, instead of trying to plug in numbers in formulas, you try plugging in a solution of the form ##y=(t-2)^r## and see what happens you will answer your own question.
     
  4. Jul 31, 2016 #3
    oh wow, that's brilliant! it worked! but can you explain more on why you chose this approach?

    thank you :smile:
     
  5. Aug 1, 2016 #4

    LCKurtz

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    If you look in your text where they derive the indicial equation, I bet you will find that a substitution like that is where the indicial equation comes from. This is an example where it is much better to understand the method than to memorize the resulting formula.
     
  6. Aug 2, 2016 #5
    Ops my bad. it's just that we were not required to get a textbook for the class and I was only referring to my notes.
    is there any book you recommend?
     
  7. Aug 3, 2016 #6

    LCKurtz

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    There are lots of online notes about it. One such is
    http://math.arizona.edu/~rjenkins/files/422/hw6soln.pdf [Broken]
     
    Last edited by a moderator: May 8, 2017
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