1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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:
    http://cwcsrv11.cwc.psu.edu/webwork2_files/tmp/equations/3c/1e4624e0fc726276872050e3ffe28d1.png [Broken]
    with initial conditions http://cwcsrv11.cwc.psu.edu/webwork2_files/tmp/equations/77/41b1266f6e87bb1b57dd6883644c521.png [Broken]

    The solution is of the form: http://cwcsrv11.cwc.psu.edu/webwork2_files/tmp/equations/b5/d7df51334509f4e8eb7c12482421651.png [Broken]
    or suitable constants http://cwcsrv11.cwc.psu.edu/webwork2_files/tmp/equations/ba/23a25f303b1dfba5efa3cc7dbfba401.png [Broken] with http://cwcsrv11.cwc.psu.edu/webwork2_files/tmp/equations/8d/8623a3204922fa8125ce9b843a6b9b1.png [Broken]
    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!
    Last edited by a moderator: May 2, 2017
  2. jcsd
  3. Mar 25, 2006 #2


    User Avatar
    Science Advisor
    Homework Helper

    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


    User Avatar
    Science Advisor

    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?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook