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Math Help - Undetermined Coefficients

  1. #1
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    Undetermined Coefficients

    Set up the correct linear combination of functions with undetermined literal coefficients to use in finding a particular integral by the method of UC. (Do not actually find the particular integrals.)

    y''-6y'+8y = x^3+x+e^{-2x}

    m^2-6m+8=0

    y_c=C_1e^{2x}+C_2e^{4x}

    S_1=(x^3,x^2,x,1)
    S_2=(x,1)
    S_3=(e^{-2x})

    S_2 is completely contained in S_1 but none are included in the complimentary function?

    Thanks.
    Last edited by JJ007; March 6th 2011 at 12:53 PM.
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  2. #2
    Behold, the power of SARDINES!
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    Quote Originally Posted by JJ007 View Post
    Set up the correct linear combination of functions with undetermined literal coefficients to use in finding a particular integral by the method of UC. (Do not actually find the particular integrals.)

    y''+6y'+8y = x^3+x+e^{-2x}

    m^2-6m+8=0

    y_c=C_1e^{2x}+C_2e^{4x}

    S_1=(x^3,x^2,x,1)
    S_2=(x,1)
    S_3=(e^{-2x})

    S_2 is completely contained in S_1 but none are included in the complimentary function?

    Thanks.
    You have a typo in your characteristic equation. It should read

    m^2+6m+8=(m+2)(m+4)
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  3. #3
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    Quote Originally Posted by TheEmptySet View Post
    You have a typo in your characteristic equation. It should read

    m^2+6m+8=(m+2)(m+4)
    Sorry. The typo was in the original equation. So it's still (m-2)(m-4).
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  4. #4
    Behold, the power of SARDINES!
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    Since the complimentary solution does not appear in the right hand side you can just "guess" the most simple form

    y=Ax^3+Bx^2+Cx+D+Me^{-2x}
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