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Find the solution to the following lhcc recurrence, confused!

  1. Mar 25, 2006 #1
    ello ello!
    I ran into this problem and i went in circles trying to figure it out. Anyone have any suggestions?
    Here is what i have:
    Find the solution to the following lhcc recurrence:
    [​IMG]
    with initial conditions [​IMG]

    The solution is of the form: [​IMG]
    or suitable constants [​IMG] with [​IMG]
    Find these constants.
    [tex]r_1 = r_2 = \alpha_1 = \alpha_2 =[/tex]

    Okay so I plugged the 2 inital conditions in for the solution form and got:
    1 = [tex]\alpha_1[/tex] + [tex]\alpha_2[/tex]
    4 = [tex]\alpha_1[/tex]*r1 + [tex]\alpha_2[/tex]*r2

    I can't solve t hat, too many unkowns and not enough equations. I also tried to find a2,a3,a4, then putting it all in terms of a0 and a1, then i was like urnt, what now? THanks!
     
  2. jcsd
  3. Mar 25, 2006 #2

    Tide

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    You should have found specific values for the r's (4 and 3) before applying the initial conditions and you have a simple system of two equations and two unknowns (the alphas).
     
  4. Mar 26, 2006 #3
    Thanks for the responce Tide but i'm still alittle lost.
    I usually found the R's when they gave me an equation like r^2+4r+2 = 0, then just solve for r to find r1 and r2. How did u figure out r1 = 4 and r2 = 3?
     
  5. Mar 27, 2006 #4

    HallsofIvy

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    Did you notice that while you used the initial conditions, you didn't use the recurrance itself anywhere? What happens if you plug
    an= rn into the recurrance equation?
     
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