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Math Help - differentiation

  1. #1
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    differentiation

    Hi, I have this initial value problem: f''(x)+4f'(x)+5f(x)=0 with f(0)=1 and f'(0)=-2

    I need to show that f(x)=cos(x)/e^2x is a solution to this initial value problem.


    then find the domain of this solution..

    Pls help, thanks!
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  2. #2
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    Quote Originally Posted by tim_mannire View Post

    I need to show that f(x)=cos(x)/e^2x is a solution to this initial value problem.
    first step is to find f'(x) and f''(x)
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  3. #3
    MHF Contributor harish21's Avatar
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    Quote Originally Posted by tim_mannire View Post
    Hi, I have this initial value problem: f''(x)+4f'(x)+5f(x)=0 with f(0)=1 and f'(0)=-2

    I need to show that f(x)=cos(x)/e^2x is a solution to this initial value problem.


    then find the domain of this solution..

    Pls help, thanks!
    f(x) = cosx \times e^{-2x}

    Thus

    f'(x)= (-sinx \times e^{-2x}) + (cosx \times -2e^{-2x})

    f''(x) =  (2e^{-2x} sinx- e^{-2x}cosx) + <br />
  (2e^{-2x} sinx + 4e^{-2x} cosx)

    f''(x) = 4e^{-2x}sinx - 3e^{-2x} cosx

    now you can find compute it for the IVP
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  4. #4
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    Quote Originally Posted by harish21 View Post

    now you can find compute it for the IVP
    Substitute what you have found into f''(x)+4f'(x)+5f(x) . Does it equal zero?
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