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Solution of the associated homogeneous problem

  1. Apr 22, 2009 #1
    1. The problem statement, all variables and given/known data
    Please help me with this, I would really appreciate it:

    Using the fact that y1 = x-1/2 cos x is a solution of the associated homogeneous problem, obtain the general solution of
    x2 y'' + x y' + (x2 - 1/4)y = x3/2


    3. The attempt at a solution

    Well the first thing i did was divide it by x^2 to obtain:
    y'' + 1/x y' + (1 - 1/4x2)y = x-1/2

    Then let y'' + 1/x y' + (1 - 1/4x2)y = 0

    A second solution will be given as
    y2 = y1 [tex]\int e ^ \int P(x)\frac{}{} (y1)^2[/tex] eintegral of P(x) dx [tex]\div[/tex] (y1)^2

    So here is where i have a problem, can someone please help me integrate

    y2 = x-1/2 cos x [tex]\int[/tex] - x / ( x-1/2 cos x)^2

    please help me..?
     
  2. jcsd
  3. Apr 22, 2009 #2
    Re: Integration

    Umm the first latex image generation is supposed to be an integral,
    The second is supposed to be a fraction, so e^integral of P(x) divided by (y1)^2

    And the third one is another integral.

    Sorry I dunno what happened..

    please help
     
  4. Apr 22, 2009 #3
    Re: Integration

    Umm the first latex image generation is supposed to be an integral,
    The second is supposed to be a fraction, so e^integral of P(x) divided by (y1)^2

    And the third one is another integral.

    Sorry I dunno what happened..

    please help me
     
  5. Apr 22, 2009 #4
    Re: Integration

    Umm the first latex image generation is supposed to be an integral,
    The second is supposed to be a fraction, so e^integral of P(x) divided by (y1)^2

    And the third one is another integral.

    Sorry I dunno what happened..

    please help me
     
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