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Differential Equation Help: As t approaches 0, y approaches

  1. Feb 6, 2013 #1
    1. The problem statement, all variables and given/known data

    http://edugen.wileyplus.com/edugen/shared/assignment/test/session.quest1886032entrance1_N10020.mml?size=14&rnd=1360201586591 [Broken]

    (b) Solve the initial value problem and find the critical value a0 exactly.
    y = ?​
    a0 = ?​
    (c) Describe the behavior of the solution corresponding to the initial value a0.
    y -> ? as t -> 0​

    3. The attempt at a solution

    I got part b correct but I thought I'd put it in here to help speed the process for whoever can help me.

    (b) y= -cos(t)/(t^2) + (a*pi^2)/(4t^2)

    a0 = 4/pi^2

    (c) I would think y would approach 0 as t approaches 0 but that apparently is wrong. This is where I need assistance. Any help is greatly appreciated.
     
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Feb 6, 2013 #2

    haruspex

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    I assume a = a0, so y= (1-cos(t))t-2
    Do you know an expansion for cos(t) valid in the vicinity of 0?
     
  4. Feb 6, 2013 #3
    I apologize if I seem a bit dense but could you elaborate on your question about the expansion on cos(t)? I'm not entirely sure what you're asking.
     
  5. Feb 6, 2013 #4

    haruspex

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    Taylor expansion? Power series?
     
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