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Math Help - Describe the behavior after finding the gerneral solution

  1. #1
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    Describe the behavior after finding the gerneral solution

    Consider the difference equation  U_{n+4} - A^{4} U_n = 0 where A>0. Find the gerneral solution of this equation. Describe the behavior of solution with respect to oscillation, boundedness, periodicity, and asymptotics where (1) A<1 (2) A=1 (3)A>1.


    I have this problem for my homework and I dont understand what to do. PLEASE HELP!!
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  2. #2
    MHF Contributor chisigma's Avatar
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    As formulated the solution of the difference equation is a sequence that is composed by four interleaved sequences each of them is writtten as...

    u_{i,n+1} = - \alpha\cdot u_{i,n} , \alpha = a^{4} , i=0,1,2,3 (1)

    ... and whose solution is...

    u_{i,n}= u_{i,0}\cdot (-\alpha)^{n} (2)

    Kind regards

    \chi \sigma
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