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Homework Help: Constructing a second solution

  1. Mar 22, 2014 #1
    1. Find a second solution of the differential eq. by using the formula.

    xy" + y' = 0 ; y1 = ln(x)


    y2 = y1(x) ( ∫(e-∫P(x)dx) / (y1(x)2) )dx


    I found the p(x):

    p(x) = 1/x

    and then I plug in everything into the formula:

    y2 = ln(x) ∫(e-∫((1)/(x))dx) / (ln(x)2 )dx


    = ln(x) ( ∫(e^(-ln(x))) / (x)(ln(x)2))

    = ∫ (1)/ (x)(ln(x))

    I do not know if this is correct. I'm going to need some help.

    the answer is y2 = 1

    Last edited: Mar 22, 2014
  2. jcsd
  3. Mar 22, 2014 #2
    Hang on, if P(x) = 1/x, why did you plug in ln(x) in the exponential integral term?

    Edit: Also you cant multiply ln(x) into the integral.
    Last edited: Mar 22, 2014
  4. Mar 22, 2014 #3
    sorry. typo. the ln(x) was after integration of (1/x)
  5. Mar 22, 2014 #4
    Rework the integral, i dont understand where you get that x in the denominator. An answer of y2 = 1 seems trivial..y2 could be any constant and it would satisfy the differential equation.
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