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Differential equation (to solve analytically)

  1. Feb 25, 2009 #1

    How can I solve this equation analytically?

    I have almost no idea. I thought that y might be a series.....please help :)
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
    Last edited: Feb 25, 2009
  2. jcsd
  3. Feb 25, 2009 #2


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    Science Advisor

    If you write that as [itex](x^2+ 1)dy/dx- 4xy= x^2+ x- 1[/itex] or
    [tex]\frac{dy}{dx}- \frac{4x}{x^2+ 1}y= \frac{x^2+ x- 1}{x^2+ 1}[/itex]
    a linear differential equation. Then
    [tex]e^{\int {4x}{x^2+1} dx}[/tex] is an integrating factor. Multiplying the entire equation by it will make the left side an "exact" derivative.
  4. Feb 25, 2009 #3


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    Gold Member

    Let me just clarify that integrating factor for you ivy =] [tex]e^{- \int \frac{4x}{x^2+1} dx}[/tex]
  5. Feb 25, 2009 #4
    Allright :) Thanks peeps!
  6. Feb 25, 2009 #5


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    Science Advisor

    Dang! Dropped a sign, didn't I?
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