Differential equation using laplace

  • Thread starter seang
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  • #1
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Homework Statement


How do I solve the following differential equation with the Laplace Transform:?
f(t)'' - a*f(t) = 0 (all ICs are equal to zero).



Homework Equations





The Attempt at a Solution



So, I get something like F(s)*(s^2 - a) = 0. I don't know where to go from there.
 

Answers and Replies

  • #2
Dick
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Your equation is missing terms which correspond to the boundary behavior of f(t). F(s)=0 is not the only solution.
 
  • #3
Dick
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Hmmm. If as you say all IC's are 0. f(0)=f'(0)=0. Then f(t)=0 is the only solution. Pretty trivial use of laplace transforms.
 

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