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Can someone verify my solution?

  1. Aug 1, 2009 #1
    I think there may be a typo in the book, I'm pretty sure I'm doing this correctly.

    Use the Laplace transform to solve the IVP: y"-6y'+9y=t; y(0)=0, y'(0)=0

    My solution is e[tex]^{3t}[/tex](1/9*t - 2/27) + 1/9*t + 2/27.

    Can someone quickly solve it again for me?
     
    Last edited: Aug 2, 2009
  2. jcsd
  3. Aug 2, 2009 #2

    tiny-tim

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    Hi CentreShifter! :smile:

    y"-6y'+9y = what? :confused:
     
  4. Aug 2, 2009 #3

    arildno

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    Well, what is your differential EQUATION??

    Is it: y"-6y'+9y=0 ?

    First, we identify that [itex]Ae^{3t}[/tex] is, indeed, a double root-solution of the IVP

    In order to find a second solution, we try with:
    [tex]Bte^{3t}[/tex]
    Inserting this trial solution into our equation yields:
    [tex](6Be^{3t}+9Bte^{3t})-6(Be^{3t}+3Bte^{3t})+9Bte^{3t}=0[/tex]
    Note that simplification of the left-hand side yields:
    [tex]0=0[/tex]

    This is precisely what you should have, since you now have two arbitrary parameters, A og B, by which you may adjust your general solution, [tex]y=Ae^{3t}+Bte^{3t}[/tex], to the initial conditions.

    (Note that this will yield you y=0 as your solution, do you now realize WHY you must state precisely what your diff. eq. actually was?
     
  5. Aug 2, 2009 #4
    You are both absolutely correct. I was the end of my study session, there should definitely be an equation there. I'll be posting it as soon as I can get to the book.

    @arildno - I know this doesn't help right now, but the problem is to be solved using Laplace transforms, not undetermined coefficients (although I suppose t doesn't really matter as long as the solution is correct).

    Edit: I have fixed the equation in the first post. It's now correct.
     
    Last edited: Aug 2, 2009
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