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Math Help - Domain of an ODE

  1. #1
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    Domain of an ODE

    I am not understanding how the domain is supposed to work. I know that x cannot be 0, but I'm confused about the interval. Looking at the direction field for the solution that goes through (-1,1), I see a parabola that seems to be bounded by x=-2 and x=0. What does this mean in terms of the domain?

    \frac{dy}{dx}=(1+x)(1+y)^2, \;\; y(-1)=1
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  2. #2
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    OK, perhaps I was being too vague? Is the domain x<0?
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  3. #3
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    Alright, then I would just solve it:

    y(x)=-\frac{2+2x+x^2}{x(2+x)}

    Bingo: x\notin\{0,-2\}
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  4. #4
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    Looks like I made an algebraic error, getting y=-\frac{2}{x^2}-\frac{1}{x}-1. So the domain would be -2<x<0, then? That would make sense with regards to the direction field.
    Last edited by petition Edgecombe; October 4th 2008 at 03:23 PM.
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