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Math Help - second order inhomogeneous equations with constant coeffiecients

  1. #1
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    second order inhomogeneous equations with constant coeffiecients

    need help with this question plz
    Attached Thumbnails Attached Thumbnails second order inhomogeneous equations with constant coeffiecients-untitled.bmp  
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  2. #2
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    Quote Originally Posted by mark18 View Post
    need help with this question plz
    This is routine application of the theory that will be in your class notes and/or textbook. Please show your working and where you're stuck.
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    y'' - y' - 2y = 0

    let y = e^(kt)
    y' = k.e^(kt)
    y'' = k^2.e^(kt)

    k^2.e^(kt) - k.e^(kt) - 2e^(kt) = 0

    e^(kt) (k^2 - k -2) = 0
    e^(kt) cant = 0
    therefore k^2 - k -2 = 0
    k = 2 or -1

    therfore Yh = Ae^2t + Be^-t

    f(t) = 6t^2 - 1
    guess Yp = Ct^2 + Dt + E
    Yp' = 2Ct + D
    Yp'' = 2C

    sub back into original equation
    (2C) - (2Ct + D) - 2(Ct^2 + Dt + E) = 6t^2 - 1

    2C(1-t-t^2) + D(-1-2t) - 2E = 6t^2 - 1

    dont know how to find C D or E
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  4. #4
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    Quote Originally Posted by mark18 View Post
    y'' - y' - 2y = 0

    let y = e^(kt)
    y' = k.e^(kt)
    y'' = k^2.e^(kt)

    k^2.e^(kt) - k.e^(kt) - 2e^(kt) = 0

    e^(kt) (k^2 - k -2) = 0
    e^(kt) cant = 0
    therefore k^2 - k -2 = 0
    k = 2 or -1

    therfore Yh = Ae^2t + Be^-t

    f(t) = 6t^2 - 1
    guess Yp = Ct^2 + Dt + E
    Yp' = 2Ct + D
    Yp'' = 2C

    sub back into original equation
    (2C) - (2Ct + D) - 2(Ct^2 + Dt + E) = 6t^2 - 1

    2C(1-t-t^2) + D(-1-2t) - 2E = 6t^2 - 1 Mr F says: Wrong move. The right move is below.

    dont know how to find C D or E
    t^2 (-2C) + t(-2C - 2D) + (2C - D - E) = 6t^2 - 1.

    Equate coefficients of powers of t:

    -2C = 6 .... (1)

    -2C - 2D = 0 .... (2)

    2C - D - E = -1 ... (3)

    Solve equations (1), (2) and (3) simultaneously.
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  5. #5
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    can u tell me if this is correct plz

    C = -3
    D = 3
    E = -8
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  6. #6
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    Quote Originally Posted by mark18 View Post
    can u tell me if this is correct plz

    C = -3
    D = 3
    E = -8
    You've solved the three equations correctly.

    By the way, I doubt I'm very much better than you at checking by simple substitution into the equations ....
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