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Slope fields

  1. May 26, 2004 #1
    I'm still having trouble with figuring out slope fields.

    If I have a function dy/dt= f(t,y), how would I go about graphing the slope field for my solutions without the use of a calculator.

    An example would be how would I graph the slope field of dy/dt = t^2-t and dy/dt = y^2? Thanks.
     
  2. jcsd
  3. May 28, 2004 #2

    HallsofIvy

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    Choose a number of (t,y) points on your graph. Calculate f(t,y) for each of those. Draw a short line through (t,y) with slope f(t,y).

    For example, at (1,1) with dy/dt= t2- t, dy/dt= 0 so we draw a horizontal line- in fact, since y is not explicitely in that formula, it is obvious that dy/dt= 0 for all points on the vertical line t=1. At each point on that line, draw a short horizontal line. At t= 0.5, t2= .25-.5= -.25 so at every point on the vertical line t= 0.5, draw a short line with slope -.25. Try to connect those to the lines at t= 1.

    For dy/dt= y2, since t does not appear explicitely, you can calculate y2 for each y and draw short lines with that slope all along the horizontal line at y.
     
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