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Calc AB Differential Equation

  1. Feb 23, 2012 #1
    1. The problem statement, all variables and given/known data

    The rate of change of the amount of material in a jar is proportional to the square of the amount present with proportionality constant k=-3.

    i) Write a differential equation for this situation
    ii) Solve the differential equation AND find y if y=1 when t=1/3

    2. Relevant equations
    Not sure of the specific equation, but I know it has something to do with exponential equations


    3. The attempt at a solution

    dy/dt=-3y^2

    seperate variables, integrate both sides, That's as far as I got, sorry :[
     
  2. jcsd
  3. Feb 23, 2012 #2

    Mark44

    Staff: Mentor

    Your diff. equation is right. When you separated variables, what did you get?
     
  4. Feb 23, 2012 #3
    dy/y^2=-3dt

    Integrating both sides yielded -1/y=-3t+C
     
  5. Feb 24, 2012 #4

    Mark44

    Staff: Mentor

    So 1/y = 3t - C = 3t + C*, where C* is just another constant.
    Now solve for y.
     
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