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First Order Diff. Eqn w/ Inital Value

  1. Apr 15, 2008 #1
    1. The problem statement, all variables and given/known data

    dy/dt = ty(4-y)/3

    y(0) = y_o

    Suppose y_o = 0.5. Find the time T at which the solution first reaches the value 3.98

    2. Relevant equations

    I separated, integrated and solved, so do i just plug in y_o wherever i see y and 0 for t to find the constant C and plug this back into my original solution? I must've got the wrong solution b/c my answer is not correct. Also, is my integral correct? I wasn't sure how to do it

    3. The attempt at a solution

    dy/[y(4-y)] = t/3 dt

    After integrating both sides:

    (1/4)( ln(y) - ln(y-4) ) = (t^2)/6 + C

    Aftering combining logs and exponentiating both sides:

    y/(y-4) = e^((2t^2)/3 + 4C)
     
  2. jcsd
  3. Apr 15, 2008 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Well, what about the rest of it? What did you get for C? What was your final answer?
     
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