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Math Help - second order differential eq help

  1. #1
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    second order differential eq help

    hi can any body help with the answer to this?

    (d^2x/dy^2)+16x=16y

    How does this compare to a general second order equation?
    Are you able to predict the response x(t) when y(t) is a unit step change?
    Solve for x(t) to verify your prediction.

    any help would be appreciated.
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by al2308 View Post
    hi can any body help with the answer to this?

    (d^2x/dy^2)+16x=16y

    How does this compare to a general second order equation?
    Are you able to predict the response x(t) when y(t) is a unit step change?
    Solve for x(t) to verify your prediction.

    any help would be appreciated.
    yes, it compares to the geenral second order ODE. just take the middle term in your characteristic equation to be zero
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  3. #3
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    Ok,

    M^2 = -16

    so M=+/- j4

    which means

    Xc= Acos4X + BSin4X

    for Xp

    16Xp=16y=16
    Xp=1

    x= 1 + Acos4x + Bsin4X

    x(0) = 1 + A + B

    X'(0) = -2Asin4x +2Bcos4x


    is this correct?
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  4. #4
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    Quote Originally Posted by al2308 View Post
    Ok,

    M^2 = -16

    so M=+/- j4

    which means

    Xc= Acos4X + BSin4X

    for Xp

    16Xp=16y=16
    Xp=1

    x= 1 + Acos4x + Bsin4X

    x(0) = 1 + A + B

    X'(0) = -2Asin4x +2Bcos4x


    is this correct?
    Clearly your Xp does not work - did you check it by substitution into the DE?

    Xp = 16y.
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