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Homework Help: D.E. laplace inverses

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

    I have two problems i cant figure out , laplace inverse of 1/(s^2-6s+10) and laplace inverse of s/(s+1)^2

    2. Relevant equations

    I use the table of laplace transforms in my book

    3. The attempt at a solution

    For the first one i did the quadratic formula to solve for s but i still couldnt figure out the answeer

    And the second one i split up the denominator and was thinkin a=-1 and b=-1 but i didnt get the right answer....im really having a hard timewith this stuff i feel like im making it harder than it really is please help
  2. jcsd
  3. Apr 24, 2012 #2


    Staff: Mentor

    For the first, 1/(s^2-6s+10) = 1/( (s - 3)2 + 1). You can think of this as F(s - 3), where F(s) = 1/(s2 + 1). I think this is the direction you should take, but I haven't worked this one through.

    For the second one, I don't think you set up your partial fraction decomposition correctly. If you wrote it as
    $$\frac{s}{(s + 1)^2} = \frac{A}{s+1} + \frac{B}{s+1}$$

    that is incorrect.
    It should be

    $$\frac{s}{(s + 1)^2} = \frac{A}{s+1} + \frac{B}{(s+1)^2}$$
  4. Apr 24, 2012 #3
    ya i realized the first one you have to complete the square but for i haven't reworked the second one i'll try the partial fractions and see if it works out......thanks for the help!
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