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Homework Help: Diff eq directional field

  1. Sep 17, 2006 #1
    Draw a direction field for the given differential equation. Based on the the direction field, determine the behavior of y at t goes to infinity. If this behavior depends on the initial value of y at t=0, describe the dependency.
    y'= -1-2y


    In class we did examples where we had a range. Like we were given y'=2y-3 and told to draw the direction field for -2<y<2 and -2<t<2.
    So for the problem above, how would I find a range, since it wants to infinity?
     
  2. jcsd
  3. Sep 17, 2006 #2

    HallsofIvy

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    Science Advisor

    "t going to infinity" doesn'g mean anything here. Your direction field is a graph in an xy-coordinate system and t doesn't have anything to do with it. At every (x, y) point, you want to draw a short vector having slope
    [itex]\frac{dy}{dx}[/itex]. But you are told that the slope is -1- 2y which depends on x only. Should be easy to draw.
     
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