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Homogeneous Linear DE's - solving IVP's

  1. Sep 30, 2009 #1
    Homogeneous Linear DE's -- solving IVP's

    1. The problem statement, all variables and given/known data

    Solve the given IVP:

    d^2y/dt^2 - 4 dy/dt -5y = 0; y(1)=0, y'(1)=2


    2. Relevant equations

    N/A

    3. The attempt at a solution

    I've solved and got the general solution y=c1e5t+c2e-t

    I'm plugging in the following to solve for my two constants:

    y(1)=0=c1e5+c2/e

    y'(1)=2=5c1e5-c2e

    So I have a system of 2 linear equations, and I can just add the two together and get:

    2=6c1e5

    and solving for c1 = e5/3

    I would go on and solve for c2, but I checked the back of the book and they have:

    y = 1/3e5(t-1)-1/3e-(t-1)

    How did they get c1 = 1/3 and e5(t-1) ?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Sep 30, 2009 #2

    tiny-tim

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    Hi tatiana_eggs! :smile:
    erm :redface: … c1 = e-5/3 …

    which gives the 1/3e5(t-1) in the book. :wink:
     
  4. Sep 30, 2009 #3
    Re: Homogeneous Linear DE's -- solving IVP's

    Oh my gosh... duh.. I seem to be slowly losing my algebra skills as I learn more and more math.

    Thanks so much!
     
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