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Diff Eq- Nonhomogeneous Equations

  1. Feb 16, 2012 #1
    1. The problem statement, all variables and given/known data
    Find a particular solution of the given equation.
    [tex] y^''' + 4y^' = 3x-1[/tex]
    2. Relevant equations

    [tex] r^3 + 4r = 0 [/tex]
    [tex] r = 0, r = 2i, r = -2i[/tex]

    3. The attempt at a solution
    [tex]y(x) = Ax-B[/tex]
    [tex]y^'(x) = A[/tex]
    [tex]y^''(x) = 0[/tex]
    [tex]y^'''(x) = 0[/tex]


    The answer is:
    [tex]y(x)=(3/8)x^2 - (1/4)x[/tex]
    But I'm not sure how they came to this, please help!!!
     
  2. jcsd
  3. Feb 16, 2012 #2

    LCKurtz

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    r=0 gives a constant as a solution of the homogeneous equation. So instead of trying Ax+B you must multiply by x and try ##y_p=Ax^2+Bx##.
     
  4. Feb 16, 2012 #3

    LCKurtz

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    The same way you started the other one. You find the complementary solution and then use Undetermined Coefficients for the particular solution. Surely your text discusses the method of Undetermined Coefficients, doesn't it?
     
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