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How can you determine y's behavior from a direction field graph?

  1. Nov 22, 2009 #1
    How can you determine y's behavior from a direction field graph??

    lets say i have the equation y' = 3 + 2y and i make a direction field graph.

    I find equilibrium position at y = -3/2.

    If question asks me to determine behavior of y as t approaches infinity, isnt this impossible, without solving the equation?

    If i follow along the graph so that t is really big, then the graph still looks the same: a horizontal line at y = -3/2, where the slope of graph is zero. So how can i infer anything about y's behavior without first solving for y?
     
  2. jcsd
  3. Nov 23, 2009 #2

    HallsofIvy

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    Re: How can you determine y's behavior from a direction field graph??

    No, the graph is NOT "a horizontal line at y= -3/2". That line is a part of the direction field graph and you can conclude from it that "if y= -3/2 for any t then it will remain -3/2 for all t". But what if the initial value of y is NOT -3/2?

    What does the direction field graph look like for y> -3/2? If y(0)> -3/2, what happens to y(t)?

    What does the direction field look like for y< -3/2? If y(0)< -3/2, what happens to y(t)?
     
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