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Homework Help: Integration Problem

  1. Apr 14, 2008 #1
    HI there!! i was wondering if you could help me with this..

    how do you integrate -2xy/(1+x^2)?

    Thank you.
     
  2. jcsd
  3. Apr 14, 2008 #2

    Hootenanny

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    Welcome to the forums,

    Your question is incomplete. What are you integrating with respect to? Is y a function of x or vice versa?

    As an aside, feel free to post a new topic for each new question, you don't need to tag your question on the end of others/
     
  4. Apr 14, 2008 #3
    Hey!

    Thanks for the quick reply.. Coz it a similar qns so i posted together with this. That equation is the gradient of a curve. So it's just to integrate with respect to x? How do you go about doing it?

    Thank you.
     
  5. Apr 14, 2008 #4
    Anyways this is the whole qns.

    find the equation of the curve in the xy plane that passes through (1,2) and whose tangent line at a point (x,y) has a slope of -2xy/(1+x^2).
     
  6. Apr 14, 2008 #5

    Hootenanny

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    Thanks, it's always a good idea to post the entire question. So you know that,

    [tex]\frac{dy}{dx} = -\frac{2xy}{1+x^2}[/tex]

    Which is a first order ODE. What methods do you know for solving first order ODE's?
     
  7. Apr 14, 2008 #6
    by using variable separable method?
     
  8. Apr 14, 2008 #7
    is the answer y(1+x^2)= c?
     
  9. Apr 15, 2008 #8

    HallsofIvy

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    You have not yet used the fact that the curve passes through (1, 2).
     
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