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Thread: Non-homogeneous recurrence relation (form question)...

  1. #1
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    Exclamation Non-homogeneous recurrence relation (form question)...

    Consider 2an = 7an-1 - 3an-2 + 2n.

    Writing down the associated homogeneous recurrence relation (to this non-homogeneous one) and the characteristic equation... does it matter which of the following I choose?

    Homogeneous: 2an = 7an-1 - 3an-2.

    I'm guessing 2an still makes a valid homogeneous recurrence relation (for whatever reason?) and doesn't strictly have to be of the form... "an = ... ".

    Characteristic: x2 = 7x - 3.

    Or...

    Homogeneous: an = (7/2)an-1 - (3/2)an-2.

    Characteristic: x2 = (7/2)x - (3/2).

    Yes, I want to know 'cause obviously the first form won't be as ugly to solve.
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  2. #2
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    Re: Non-homogeneous recurrence relation (form question)...

    How about:
    $2x^2=7x-3$?

    Then, you have $2x^2-7x+3=0 \Longrightarrow (2x-1)(x-3) = 0$, $x=\dfrac{1}{2}$ or $x = 3$.
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  3. #3
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    Re: Non-homogeneous recurrence relation (form question)...

    Yes, you do have that for the characteristic.

    Another thing not properly shown to me.
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