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Use of laplace to solve a differential equation

  1. Dec 18, 2009 #1
    I was asked to use a laplace transform to solve d^2x/dt^2 - 3(dx/dt) - 10x = e^-t
    with the initial conditions x(0) = 0 and x'(0) = 0

    I got down to (s^2)x(s) - sx(0) - x'(0) - 3(sX(0) - x(0)) - 10X =1/(s+1)

    I tried plugging in the initail conditions and didnt get the answer I was supposed to, think I have gone wrong somewhere if someone can help me out
     
  2. jcsd
  3. Dec 18, 2009 #2
    Got it wrong. That's:
    [tex]s^{2}X(s)-sx_{0}-x'_{0}-3(sX(s)-x_{0})-10X(s)=1/(s+1)[/tex]
    With the boundary conditions, you get
    [tex]X(s)=\frac{1}{(s+1)(s^{2}-3s-10)}[/tex]
     
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