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Homework Help: Integrating factor for solving equation problem.

  1. Dec 6, 2008 #1
    1. The problem statement, all variables and given/known data

    Find the gerneral solution of the differential equation below:
    dy/dt=(-y/t)+2

    2. Relevant equations

    none

    3. The attempt at a solution



    my solution by using integrating factor:
    1.find the homogenous solution first
    dy/y = -1/t dt
    you get ln(y) = -ln(t) when integrating both side.
    you get y = -t

    2. find gerenal soultion:
    u(t) = 1/y(homogenous)
    so in this case u(t) =1/-t, b(t) = 2

    now apply integrating method:
    (u(t)y(t))' = u(t)b(t)
    (y(t)/-t)' = 2/-t
    taking integral of both side we get
    y(t)/-t = -2ln(t)+c = -ln(t^2)+c
    then Y(t) = -t(-ln(t^2)+c) = -tln(t^2)+-tc
    we get y(t) = -tln(t^2)+-tc for general solution.

    but the book answer is y(t) = t+c/t

    so did I do anything wrong, I dont really find anything wrong myself.
     
  2. jcsd
  3. Dec 7, 2008 #2
    It is not ln(-t), it is -ln(t).

    Shouldn't u(t) = 1/t just by reading off the differential equation?

    Differentiate, not integrate.
     
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