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Math Help - Difference Equation

  1. #1
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    Difference Equation

    i have to solve Xn+1 -4Xn +3Xn-1= 36n^2
    I did the first part, where i find Xn=A3^n+ B
    But when i try to find the solution of the form Xn= Pn^2+ Qn+ R
    it turned out weird and i cannot find the P Q R,can anyone help me?


    If possible, can someone post a full answer for me? I really need an example for this kind of question.
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Re: Difference Equation

    Quote Originally Posted by kanezila View Post
    I did the first part, where i find Xn=A3^n+ B
    Right

    But when i try to find the solution of the form Xn= Pn^2+ Qn+ R
    it turned out weird and i cannot find the P Q R,can anyone help me?
    The characteristic equation is \lambda^2-4\lambda +3=0 , that is \lambda=1 is a simple root . According to a well known theorem a particular solution is a polynomial p(n) of degree 2+1=3 .
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