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Homework Help: Undetermined Coeff.

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

    (I am using b, for beta)

    Let

    [tex]f(t)=ce^{-\beta t}[/tex]

    with b a fixed number and c in R is arbitrary but given.

    Write the general solution of

    [tex]x'=-x+f(t)=-x+ce^{-\beta t}[/tex]

    Hint: Use undetermined coeff. and consider a particular solution of the form

    [tex]x_p=\alpha e^{-\beta t}[/tex]

    and determine [tex]\alpha[/tex]

    2. Relevant equations



    3. The attempt at a solution

    I have solved for

    [tex]\alpha = \frac{c}{-\beta +1}[/tex]
     
  2. jcsd
  3. Oct 7, 2008 #2

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    Hi Unassuming! :smile:

    (have an alpha: α and a beta: β :smile:)

    What's the difficulty?

    You have found a particular solution, (c/(1-β))e-βt.

    Now just find the complementary solution, ie the solution to x' = -x, and add it. :smile:
     
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