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Differential Equations: Second Order Equations

  1. Sep 3, 2011 #1
    1. The problem statement, all variables and given/known data

    Find a second order differential ewuation for which three functions y=2e^-t, y=2te^-t, y=e^(-t+1) are solutions.

    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Sep 3, 2011 #2

    LCKurtz

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    Since you didn't show us what you have tried, instead of answering your question directly, I will ask you this:

    Can you solve this de:

    y'' - 4y' + 4y = e2t

    and if so, what method would you use?

    Hint: This isn't an idle question.
     
  4. Sep 3, 2011 #3

    HallsofIvy

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    If those functions were independent, this would be impossible but [itex]e^{-t+ 1}= e^{-t}e^1= e e^{-t}[/itex], a constant times [itex]e^{-t}[/itex] so you really have only two independent solutions.

    Do you know what the "characteristic equation" of a linear differential with constant coefficients is? Such an equation will have [itex]e^{ax}[/itex] and [itex]e^{bx}[/itex] as independent solutions if and only if its characteristic equation is [itex](r- a)(r- b)= 0[/itex].
     
    Last edited: Sep 4, 2011
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