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Second order homogeneous ODE with vanishing solution

  1. Dec 7, 2011 #1
    1. The problem statement, all variables and given/known data

    Solving the linked set of ODEs:

    y" + y = 1-t^2/π^2 for 0 ≤ t ≤ π

    y" + y = 0 for t > π

    We are given the initial condition that y(0) = y'(0) = 0, and it is also noted that y and y' must be continuous at t = π

    2. Relevant equations

    See above.

    3. The attempt at a solution

    The non-homogeneous ODE when t is between 0 and π didn't give me too much trouble, but it's the seemingly simpler homogeneous case for t > π that I'm struggling with: everything seems to go to zero!

    The root of the characteristic equation is ±i.

    That gives a solution of y = A cos t + B sin t, but using the given initial conditions both A and B are 0.

    Thanks for any help you can offer.
  2. jcsd
  3. Dec 7, 2011 #2


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    The initial conditions don't matter because they're for t=0 and you're looking at the solution for t>pi.

    You want to match the solutions in the two regions at t=pi.
  4. Dec 7, 2011 #3
    Ah, thanks, that helps a lot.
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