Integration Problem

  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. Hootenanny

    Hootenanny 9,681
    Staff Emeritus
    Science Advisor
    Gold Member

    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. 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. 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. Hootenanny

    Hootenanny 9,681
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    Gold Member

    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. by using variable separable method?
     
  8. is the answer y(1+x^2)= c?
     
  9. HallsofIvy

    HallsofIvy 40,369
    Staff Emeritus
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    You have not yet used the fact that the curve passes through (1, 2).
     
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