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Homework Help: A differential equation problem

  1. Mar 27, 2007 #1
    I'm not sure how to solve the following problem. It's quite unlike the other problems I've had to solve since I started learning about differential equations. Can anybody help?

    A disease spreads at a speed that is proportional to the multiplier of healthy and sick people. Let's call the sick quotient of a group x and the quotient of healthy people 1 - x. Then we have dx / dt = kx(1 - x). If half of the group is sick and the disease spreads at a constant speed, every member of the group will be sick in 24 days time. Then we have x = 1/2 , 1 - x = 1/2 and dx / dt = (1/2)/24 = 1/48 , so 1/48 = k * 1/2 * 1/2 <=> k = 1/12 , which gives dx / dt = 1/12 x(1 - x). Calculate how big a fraction of the group is sick in 12 days time.
    Last edited: Mar 27, 2007
  2. jcsd
  3. Mar 27, 2007 #2
    Hint: Separate the variables and then integrate, do you know how to integrate partial fractions?
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