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Differential Equation ?

  1. Apr 19, 2008 #1
    1. The problem statement, all variables and given/known data

    Solve (x^2 + y^2 - y)dx + x dy = 0 when x > 0, y > 0.

    2. Relevant equations

    (x^2 + y^2 - y)dx + x dy = 0

    3. The attempt at a solution

    dy/dx = - (x^2 + y^2 - y) / x
    That seems like a tricky one. Can I make it a second-order diff. eq.?
    Well, with the topic we have had about vectorfields I can backwards engineer it into
    F(x,y) = (x^2 + y^2 - y)i + (-x)j
    But that dosn't make much sense to me.
     
  2. jcsd
  3. Apr 19, 2008 #2
    (Hmm, I miss an edit-button...)

    I shorted it down to x dy/dx = -x^2 - y^2 + y or dy/dx = -x -y^2/x + y/x
     
  4. Apr 19, 2008 #3

    Defennder

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    You don't have to complicate this one unnecessarily. The substitution y=vx works fine here.
     
  5. Apr 19, 2008 #4

    Shooting Star

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    [tex](x^2+y^2)dx + (xdy-ydx) = 0 =>
    dx + \frac{xdy-ydx}{x^2+y^2} = 0.[/tex]

    Whenever you get (xdy-ydx), see if you can make it into the form

    [tex]\frac{xdy-ydx}{x^2}[/tex], since that is equal to [tex]d(\frac{y}{x}).[/tex]

    See if you can spot a function of (y/x) with the d(y/x) here.
     
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