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Math Help - Annihilator Method?

  1. #1
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    Annihilator Method?

    Is there anyone well versed in the annihilator method? I don't think I quite fully understand it, and the given problem that we have is:



    Solve the given differential equation using the annihilator method

    y" - 3y' - 4y = 5e (raised to the) -t

    Note: In this case, you have the provide the general solution of the problem.



    Any help is appreciated. Thank you!
    --Rachel
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  2. #2
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    Quote Originally Posted by tibetan-knight View Post
    Is there anyone well versed in the annihilator method? I don't think I quite fully understand it, and the given problem that we have is:



    Solve the given differential equation using the annihilator method

    y" - 3y' - 4y = 5e (raised to the) -t

    Note: In this case, you have the provide the general solution of the problem.
    No, I don't- you do!

    Write this equation in "operator form" as D^2y- 3Dy- 4y= 4e^{-t} which can then be factored as (D- 4)(D+ 1)y= 4e^{-t}
    Since the derivative of [itex]e^{-t}[/itex] is [itex]-e^{-t}[/itex] it can be "annihilated" by D+1: [itex](D+1)(4e^{-t}= 0[/itex]. That tells us that (D+1)[(D-4)(D+1)y= (D+1)(4e^{-t} so (D- 4)(D+1)^2y= 0. Can you solve that?

    The general solution to that will have three unknown constants. One of them will be determined by the fact that y must actually satisfy the original equation.


    Any help is appreciated. Thank you!
    --Rachel
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