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Have I got this right?

  1. Apr 30, 2006 #1
    I'm given the differential equation dy/dx = 0.2y - 0.02x and I am asked to obtain a straight line equation for dy/dx = 0.5

    Does this mean need to solve the quadratic 0.2y - 0.02x - 0.5 = 0 ?
     
  2. jcsd
  3. Apr 30, 2006 #2

    Hootenanny

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    I hate to burst your bubble but
    Isn't a quadratic. Is the question phrased exactly as you have typed?

    ~H
     
  4. Apr 30, 2006 #3
    Well the whole exercise is as follows:

    The spread of a disease in a community is modelled by the following differential equation:

    dy/dx = 0.2y - 0.02x where y is the number of infected individuals in thousands, and x the time in days.

    1) Show the equation that for the family of 'curves' in the plane for which dy/dx is a constant, is the form y=mx+c.

    2) Obtain the four straight line equations for dy/dx equal to 0.5, 1, 2 and 3

    3) Solve the equation using the linear 1st order method, given that initially there are on thousand infected individuals.

    Help please :-)
     
  5. Apr 30, 2006 #4

    Hootenanny

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    Ok, for question two, it is basically asking you to find the equation of a straight line for when the rate of infection is 500 infections per day. So what you did above; 0.2y - 0.02x - 0.5 = 0 is correct. Simply re-arrange this into the form y = mx +c.

    ~H
     
    Last edited: Apr 30, 2006
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