1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    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

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Taylor expansion? Power series?
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook




Loading...