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Integral curves

  1. Jan 30, 2012 #1

    fluidistic

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    1. The problem statement, all variables and given/known data
    Find the solution to [itex]y'=\frac{y+x}{y-x}[/itex] and graph the integral curves.


    2. Relevant equations
    Exact differential equation.


    3. The attempt at a solution
    I noticed it's an exact differential equation, I solved it implicitely. I reached that [itex]\frac{y^2 (x)}{2}-\frac{x^2}{2}-yx=\text{constant}[/itex]. I've looked into wikipedia about the integral curves but I don't really know how to find them here. If I understood well, an integral curve is a solution to the DE, so here it would be any y(x) that satisfies the DE. But here I can't get y(x) explicitely, so how do I graph y(x)?... Any idea is welcome!
     
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  3. Jan 30, 2012 #2

    HallsofIvy

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    Choose a number of specific values for the constant and graph those curves.
     
  4. Jan 30, 2012 #3

    fluidistic

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    Ah I see, thank you very much. I graph point per point, maybe I'm missing an obvious curve or something.
    I take C=1. I set x=0 and I get [itex]y=\pm \sqrt 2[/itex]. I graph this in the x-y plane. Now I set x=2 and I get a quadratic equation for y, which yields [itex]y= 2 \pm \sqrt {10}[/itex]. So for a fixed C, there are 2 curves; maybe parabolas or hyperbolas.
     
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