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Wronskian Second Solution/Differential Equations

  1. Feb 26, 2009 #1
    1. The problem statement, all variables and given/known data

    Given that Φ2 = Φ1 * ∫ e^(-∫a(x)dx)) / (Φ1)^2 dx

    and Φ1 = cos(ln(x)), a = 1/x, solve for Φ2.

    2. Relevant equations

    3. The attempt at a solution

    Φ2 = cos(ln(x)) * ∫ e^(-∫1/x dx)) / cos^(2)(ln(x)) dx

    = cos(ln(x)) * ∫ e^(-ln(x)) / cos^(2)(ln(x)) dx

    = cos(ln(x)) * - ∫ x / cos^(2)(ln(x)) dx

    My problem begins here with trying to solve for that integral. I don't have the slightest idea where to begin, except maybe integration by parts.
  2. jcsd
  3. Feb 26, 2009 #2


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    Gold Member

    I believe you have expanded your brackets in the exponential wrong [tex]e^{-ln(x)}[/tex] does not equal [tex]-x[/tex] but rather [tex]e^{ln(x^{-1})}[/tex] which is of course [tex]\frac{1}{x}[/tex] in which case a simple u substitution will work
  4. Feb 26, 2009 #3
    Thanks for catching that mistake.
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