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Solve the First Order Linear D.E. with the initial value

  1. Apr 14, 2013 #1
    1. The problem statement, all variables and given/known data

    dy/dt=y(9-y)

    y(0)=2

    2. Relevant equations



    3. The attempt at a solution

    dy/(y(9-y)) = dt
    ∫dy/(y(9-y)) = ∫dt

    partial fraction decomposition
    1=A/y + B/(9-y)
    1=9A-Ay +By
    1/9=A
    0=1/9 +B
    B=-1/9

    1/9∫1/y -1/9∫1/(9-y)=t+C
    1/9ln|y| -1/9(ln|9-y|)
    1/9(ln|y/(9-y)|)=t+C
    y/(9-y) =Ke^(9t)
    2/7=K

    y/(9-y) =(2e^(9t))/7

    I'm stuck right here. It's a little embarrassing, but I forgot how to find the solution here.
     
  2. jcsd
  3. Apr 14, 2013 #2
    You're close. Start by multiplying both sides by (9-y), distribute, add a certain term to both sides, factor out a y, etc.
     
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