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Differential equation query

  1. Jan 24, 2012 #1
    Hello, regarding the differential equation: "dy/dx = -x/y"
    The general solution is y^2+x^2 = c.

    I am wondering why it is expressed this way instead of "y=-x^2+c" ?
    I thought you had to seperate the x and y to opposite sides of the equation ?

    Thanks for any help.
     
  2. jcsd
  3. Jan 24, 2012 #2

    tiny-tim

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    hello fran1942! :smile:

    (you mean y = √(c - x2) :wink:)
    no, there's nothing special about y …

    the answer is a curve (in this case, a circle), and x2 + y2 = c is a more natural way of describing a curve :wink:
     
  4. Jan 25, 2012 #3
    dy/dx = -x/y
    y*dy = -x*dx
    y²/2= -x²/2 +C
    y² = -x² +c (c=2C)
    y²+x² = c
     
  5. Jan 26, 2012 #4

    HallsofIvy

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    Well, it wouldn't be expressed that way because those are not at all the same!
    I presume you meant [itex]y= \sqrt{c- x^2}[/itex]. The difficulty with that is that it is only "half" of the solution- the other half would be [itex]y= -\sqrt{c- x^2}[/itex].

    No, differential equations often have solutions that are not functions.
     
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