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Differential Equations? Fill in the table.

  1. May 28, 2012 #1
    Fill in the missing values in the table given if you know that dy/dt=0.2y. Assume the rate of growth given by dy/dt is approximately constant over each unit time interval and that the initial value of y is 6.

    Table:
    t-0-1-2-3-4
    y-6-?-?-?-?
    (fill in the missing values where there is a question mark)

    I got:
    t = 1, y = 7.33
    At t = 2 , y = 8.95
    At t = 3 , y =10.93
    At t = 4 , y = 13.35
    using y=6e^(.2t)

    but it is wrong, Help?
     
  2. jcsd
  3. May 28, 2012 #2

    LCKurtz

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    You have apparently just plugged the t values in to the exact solution. But that is not what the problem asks you to do. What you are asked to do looks a lot like Euler's approximation method. So start with knowing at t=0 the slope is ##.2(6)##, assume that constant slope to get the value at ##t=1##. Then do the same thing for the next steps.
     
  4. May 28, 2012 #3
    Thank you, I redid the problem using y₂ = y₁ + m(x₂ - x₁) and got:

    t --- y
    0 .. 6
    1 .. 7.2
    2 .. 8.64
    3 .. 10.368
    4 .. 12.4416

    can you please check if this is correct?
    Thank you
     
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