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Homework Help: Calculus problem

  1. Aug 31, 2004 #1
    Hi, I would need help on this problem. I have to solve this equation
    f'(x) + ((1 -2x)/x^2)*y = 1. I started the problem and I was stuck at
    y= (x^2)*e^(1/x) * integral (e^(-1/x))/(x^2) :mad: . I have no idea how to do this so if anyone knows how, it would be really appreciated.
  2. jcsd
  3. Aug 31, 2004 #2


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    Gold Member

    By "do this" I presume you mean you are having trouble finding an elementary expression for

    \int \frac{e^{-1/x}}{x^2} \, dx

    What techniques have you tried to apply?
  4. Aug 31, 2004 #3
    Try a substitution , realizing that (1/x²)dx = - d(1/x)

  5. Aug 31, 2004 #4
    (1/x²)dx = - d(1/x). Thanks a lot, I was quite lost (trying to integrate by parts...)but I finally solved it. Thanks.
  6. Aug 31, 2004 #5
    For integration by parts, try ILATE (I = Inverse Trig, L = Logarithmic, A = Algebraic, T = Trig, E = Exponential). This pretty much sums up the order in which the first function should be chosen if you wish to integrate something of the form,

    [tex]\int udv = uv - \int v du[/tex]

    (ie--how to chose u).

  7. Sep 1, 2004 #6


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    Erm, have you thought about what the derivative of:


    is? I think that will solve your problem :wink:

    Edit: Sorry, missed that you had solved it.
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