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Initial Value Problem. I'm really confused just need some help!

  1. Mar 24, 2012 #1
    1. The problem statement, all variables and given/known data

    Solve the following Initial Value problem for x(t) and give the value of x(1)

    2. Relevant equations

    (dx/dt)-xt=-t , x(0)=2

    3. The attempt at a solution

    (dx/dt)-xt = -t
    (dx/dt) = xt-t
    (dx/dt) = t(x-1)
    (1/(x-1)) (dx/dt) = t
    (1/(x-1)) dx = t dt

    Then I integrate both sides.

    ∫(1/(x-1)) dx = ∫t dt
    ln[x-1] + C = (1/2)t^2

    I put x=2 and t=0
    ln[1] + C = (1/2)(0)^2
    0 + C = 0
    C = 0




    So my problem is the x(1) bit... I don't know where to go with this... would I just make t=1 and solve for x and give a numerical answer by subbing i back in?
    Or am I way of the mark and have everything wrong :O
     
  2. jcsd
  3. Mar 24, 2012 #2

    tiny-tim

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    Science Advisor
    Homework Helper

    welcome to pf!

    hi mazz1801! welcome to pf! :smile:

    (try using the X2 button just above the Reply box :wink:)
    ("subbing i"? :confused:)

    yes, that's fine :smile:

    you should now get rid of the ln by writing x-1 = et2/2

    then put t = 1
     
  4. Mar 24, 2012 #3
    Thank you very much tiny-tim :)
     
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