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Variation of Parameters

  1. Apr 11, 2005 #1
    I'm trying to understand this concept. Jere's the problem i'm doing.
    I have to find the general solution for:
    y'' + 36y = -4xsin(6x)

    So you then solve for your characteristic equation and get lamda = +/- 6
    so y1 = e^-6x and y2 = e^6x
    You get your matrix for w, w1, and w2.
    w = 12
    w1 = 4xe^6xsin(6x)
    w2 = -4xe^-6xsin(6x)

    I have the problem at getting u1 and u2.
    u1 = 1/3 the integral of xe^6xsin(6x) dx
    u2 = -1/3 the integral of xe^-6xsin(6x) dx

    How do you do that integration?

    Thanks for your help,
  2. jcsd
  3. Apr 11, 2005 #2
    Your characteristic equation should be of the form y=Asin6x+Bcos6x since the the squareroot of -36 is 6i and -6i =)
  4. Apr 11, 2005 #3


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    Yeah,and Lagrange's method kicks ass.So apply it.

  5. Apr 26, 2005 #4
    I was wondering if anyone knew of any good references on solving systems of equations involving trigonometric equations. Any information would be appreciated.
  6. Apr 26, 2005 #5
    Found the answer - I had forgotten Cramer's rule.
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