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Thread: Recurrance Relation

  1. #1
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    Recurrance Relation

    I have asked to solve the linear non-homogeneous equation.

    $\displaystyle A(n) = 8A(n-2) -16A(n-4) +F(n) , where F(n) = N^2*4^n$

    All these n are subscript of A.

    I am not sure how to resolve that F(n).

    Can anyone help me.
    Last edited by kumaran5555; Nov 14th 2010 at 10:04 PM.
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Using a well known theorem and taking into account that $\displaystyle 4$ is not a root of the charactheristic equation, a particular
    solution for the complete equation has the form $\displaystyle X(x)=(an^2+bn+c)4^n$.
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  3. #3
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    Can you please name the theorem used.
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  4. #4
    MHF Contributor FernandoRevilla's Avatar
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    If $\displaystyle F(n)=a^nP_m(n)$ where $\displaystyle P_m(n)$ is a polynomial of degree $\displaystyle m$, and $\displaystyle a$ is not a root of the characteristic equation, then a particular solution for the complete is $\displaystyle x(n)=a^nQ_m(n)$, where $\displaystyle Q_m(n)$ is a polynomial of degree $\displaystyle m$. If $\displaystyle a$ is a root of the characteristic equation with multiplicity $\displaystyle s$ then, $\displaystyle x(n)=a^mn^sQ_m(n)$.

    Regards.
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