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Homework Help: Differential Equations: Wronskian question.

  1. Jun 7, 2010 #1
    1. The problem statement, all variables and given/known data
    Hey Everyone,

    Here is a problem from my book that has my confused. I really don't understand what it wants me to do so if anyone could give me a few hints it would be greatly appreciated.

    I am doing problem 34, but I included 33 since it wanted to follow the same method.

    000004.jpg

    Sorry if I seem like I am asking you to do my homework. I'm not, just looking for a place to start.

    Thanks,
    Rob
     
    Last edited: Jun 7, 2010
  2. jcsd
  3. Jun 7, 2010 #2

    Mark44

    Staff: Mentor

    the attachment is invalid...
     
  4. Jun 7, 2010 #3
    Really? I am able to open it just fine. Can anyone else open this?

    EDIT: I take that back. It works for me in Chrome but not Firefox. I will upload it somewhere else and fix my post.
     
  5. Jun 7, 2010 #4

    Office_Shredder

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    Let's start by looking at 33. Do you know how to use the Wronskian to show that functions are linearly independent in general?
     
  6. Jun 7, 2010 #5
    Hey office_Shredder,

    I am reasonably familiar with using the Wronskian to show that functions are linearly independent. I am more used to this form:

    8d606b824d0946483b111ce8935ba568.png

    Where if W = 0 is true on an open interval I then the functions are linearly independent.

    I don't completely understand the wronskian equation given in problem 33.
     
  7. Jun 7, 2010 #6

    gabbagabbahey

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    If you define [itex]f_i(x)=\text{exp}(r_i x)[/itex], [itex]1\leq i \leq n[/itex], what is [itex]f'_i(x)[/itex]? How about [itex]f''_i(x)[/itex]? What does that make the Wronskian for the [itex]n=3[/itex] case? Is there a rule for taking determinants where a column is multiplied by some factor that might help you here?
     
  8. Jun 8, 2010 #7
    I understand where the matrix comes from now but I am not sure what method you are talking about for solving the determinant. Care to shed some light?
     
  9. Jun 8, 2010 #8

    gabbagabbahey

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    Use property 3 here. For example,

    [tex]\begin{vmatrix} a & 2b & 3c \\ 4a & 5b & 6c \\ 7a & 8b &9c \end{vmatrix}=a\begin{vmatrix} 1 & 2b & 3c \\ 4 & 5b & 6c \\ 7 & 8b &9c \end{vmatrix}=ab\begin{vmatrix} 1 & 2 & 3c \\ 4 & 5 & 6c \\ 7 & 8 &9c \end{vmatrix}=abc\begin{vmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 &9 \end{vmatrix}[/tex]
     
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