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Homework Help: Differential Equations Help

  1. Dec 31, 2009 #1
    Gday,
    Just having a problem doing the initial rearrangement, before I integrate it, of the following differential equation to get the y's and x's on the same side:

    (x2+1)y' = xy


    Can anyone help me out with this? Ive been trying all day to get both x and y on either side but I cant manage. Is there a trick to it?
    Any help appreciated!

    Thanks
    Matthew
     
  2. jcsd
  3. Dec 31, 2009 #2

    Hepth

    User Avatar
    Gold Member

    just divide?
    x/(x^2+1) = y'/y
     
  4. Dec 31, 2009 #3
    Yeh but then on the right side you have (dy/dx)/y
    How would you then get the dx over to the left side?

    Regards
     
  5. Dec 31, 2009 #4

    Hepth

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    Gold Member

    multiply

    [tex]
    \frac{x}{\left(x^2+1\right)} = \frac{1}{y} \frac{dy}{dx}
    [/tex]
    [tex]
    \frac{x dx}{\left(x^2+1\right)} = \frac{1}{y} dy
    [/tex]
     
  6. Dec 31, 2009 #5
    Okay sweet, thanks for that.
    Next dumb question, how do you integrate the left side when dx is up the top like that?

    Thanks for your help!
     
  7. Dec 31, 2009 #6

    Hepth

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    Gold Member

    there is no "up top", its all the same, its just a simple multiplication, nothing new or crazy.
    [tex]
    \frac{x}{x^2+1} dx
    [/tex]

    and try u=x^2+1
     
  8. Dec 31, 2009 #7
    Thanks man for your help! Ill have a look at it again tomorrow!
    For now, its new years eve time!!! Have fun!
     
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