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Cheeky integral

  1. May 17, 2005 #1
    Hi guys,

    In an attempt to solve the following differential equation, I have come up with an integral that has stumped me.

    The differential equation is as follows:


    \frac{dy}{dx} + \frac{y}{x^2} = 2x [/tex]

    Using an integrating factor, I end up with the following:

    [tex] y \cdot e^{-\frac{1}{x}} = 2\int xe^{-\frac{1}{x}} dx [/tex]

    I cannot solve that right hand integral, I have tried using parts and substitution and I cant really yield anything meaningful... Is it possible to evaluate this integral using basic calculus methods? Or is something else required?

    Thanks!! :biggrin:
  2. jcsd
  3. May 17, 2005 #2


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    Add a constant to this result.


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  4. May 17, 2005 #3
    I tried using the integrator from Wolfram..but I wanted to see if there was a neater result. This was actually a question on an engineering paper. Have I done steps preceeding the integral evaluation correct, with the integrating factor?

  5. May 17, 2005 #4


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    Everything is okay.Here's what Maple says

    [tex]\frac{dy}{dx}+\frac{y}{x^2}=2x [/tex]

    , Exact solution is :

    [tex]y\left( x\right) =x^2-x+e^{\frac{1}{x}}\mbox{Ei}\left( 1,\frac{1}{x}\right) +Ce^{\frac{1}{x}} [/tex]

  6. May 17, 2005 #5


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    I get the same thing as you brenden.

    Also, I wouldn't trust that integrator too much. It has hapened to me twice that he provided a wrong answer.
  7. May 17, 2005 #6
    Ok cheers fellas, must've been a type-o in the paper.

    Much appreciated.
  8. May 17, 2005 #7
    Oh by the way, I'm not sure what the equivalent is, but I am fairly proficient up to Calc III, and I want to begin pursuing some advance calculus. I am looking for a suitable text in which I can do some self study and tutor myself as best possible. Can anyone recommened a thorough and lucid text for self-study?

    I am looking for something more precise, as opposed to just a list of rules and how to implement them.

    Thanks guys, much appreciated
    Last edited: May 17, 2005
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