1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Laplace Transform (Should be easy)

  1. Mar 31, 2008 #1
    [SOLVED] Laplace Transform (Should be easy)

    1. The problem statement, all variables and given/known data
    I know there are other ways to solve this, but I HAVE to use Laplace Transform

    y''-y'-6y=0 where y(0)=2 and y'(0)=-1

    3. The attempt at a solution

    Written as Laplace:


    [tex]\Rightarrow s^2*Y(s)-s*y(0)-y'(0)-s*Y(s)+y(0)-6*Y(s)=0[/tex]

    [tex]\Rightarrow s^2*Y(s)-2s+1-s*Y(s)+2-Y(s)=0[/tex]

    [tex]\Rightarrow s^2*Y(s)-s*Y(s)-Y(s)=-3+2s[/tex]

    [tex]\Rightarow Y(s)=\frac{-3+2s}{s^2-s-1}[/tex]

    Am I missing something? The numerator and denominator don't factor. Is a separation by partial fractions my next step? Or did I miss something that would make it way easier?

  2. jcsd
  3. Mar 31, 2008 #2


    User Avatar
    Science Advisor

    What happened to the "6" on 6Y(x)?

    s2- s- 6 certainly does factor!
  4. Mar 31, 2008 #3
    Splendid!! Now too bad the numerator wasn't -3+s then I would be in business.
  5. Apr 2, 2008 #4
    I'm also having a problem with laplace transforms.

    I have an equation in the form

    I = [tex]\frac{1}{s}[/tex] - [tex]\frac{11}{3s+2}[/tex]

    Does this transform to

    I(t) = 1-11[tex]e^{-2t}[/tex]

    or do i need to try and do something with the 3?

    I think I just got it, sorry for hi-jacking you're thread.
    I(t) = 1 - 11/3 ([tex]e^{-2/3t}[/tex])
    Last edited: Apr 2, 2008
  6. Apr 2, 2008 #5

    It's cool. And you got it right it looks like!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook