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Homework Help: Nonhomogeneous linear differential equation

  1. Jan 15, 2012 #1
    1. The problem statement, all variables and given/known data
    solve for y(x).

    [tex]y"'-6y"+11y'-6=e^{4x} [/tex]

    2. Relevant equations

    Wronskian determinant. Method of variations.

    3. The attempt at a solution

    Supposing that [u', v', w'] are the solutions, wronskian det=W is [tex]10e^{6x} [/tex]
    By use of [tex] x_k=\frac{det(M_{k})}{det(x)}[/tex], I got [tex]u'=\frac{1}{4}e^{8x},v'=\frac{-1}{9}e^{9x}, w'=\frac{-1}{7}e^{7x}[/tex]. Integration gives [tex]y=\frac{1}{10}e^{2x}-\frac{1}{30}e^{3x}-\frac{e^{x}}{10}[/tex].
    Last edited: Jan 15, 2012
  2. jcsd
  3. Jan 16, 2012 #2
    The answer has four whereas i came up with only 3 since the roots are 1,2, and 3 respectively. I think [tex] W=2e^{6x} [/tex]
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