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Differential equation (to solve analytically)

  1. Feb 25, 2009 #1
    (x^2+1)y'=x^2+x-1+4xy



    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

    HallsofIvy

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    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

    djeitnstine

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    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

    HallsofIvy

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    Dang! Dropped a sign, didn't I?
     
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