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!

Differential Equations with Discontinuous Forcing Functions

  1. Nov 23, 2014 #1
    1. The problem statement, all variables and given/known data
    Solve the given initial-value problem.
    [itex] y'' = 1 - u(t-1) [/itex]
    [itex] y(0) = 0 [/itex]
    [itex] y'(0) = 0 [/itex]
    2. Relevant equations

    3. The attempt at a solution
    First I took the Laplace transform of both sides:
    [itex] \mathcal{L}(y'') = \mathcal{L}(1 - u(t-1)) [/itex]
    [itex] s^{2}Y(s) - sy(0) - y'(0) = \mathcal{L}(1) - \mathcal{L}(u(t-1)) [/itex]
    [itex] s^{2}Y(s) = \frac{1-e^{s}}{s} [/itex]
    [itex] s^{2}Y(s) = (1-e^{s})\frac{1}{s} [/itex]
    [itex] Y(s) = (1-e^{s})\frac{1}{s^{3}} [/itex]
    At this point I am sort of stuck, the solution given in the back of the book is : [itex] \frac{1}{2}t^{2} - \frac{1}{2}u(t-1)(t-1)^{2} [/itex]
    I'm having a hard time seeing how my work is going to end up as the solution given, so I am thinking maybe I didn't do something right here..
  2. jcsd
  3. Nov 23, 2014 #2
    I think I may have figured out what I was doing wrong, I forgot to factor my answer...I'll post a solution momentarily...
  4. Nov 23, 2014 #3
    Ok, so did figure out what I was doing wrong...I'm sorry if I've wasted anyone's time
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted