The discussion focuses on solving the inverse Laplace transform of the function f(s) = 6/(s^2 - 9). The solution involves factoring the denominator into (s - 3)(s + 3) and applying the inverse transform formula f(t) = (1/(b-a))(e^(-at) - e^(-bt)). The final result derived is f(t) = e^(3t) - e^(-3t). Participants confirm the accuracy of the solution by suggesting verification through the forward Laplace transform.
PREREQUISITESStudents studying differential equations, mathematicians working with transforms, and anyone seeking to deepen their understanding of inverse Laplace transforms.
Spoolx said:Homework Statement
f(s) = 6/s^2-9
Homework Equations
I think
f(t) = (1/b-a)(e^-at-e^-bt)
The Attempt at a Solution
Replace 6/s^2-9 with 6/(s-3)(s+3)
a=-3
b=3
Plug in
(1(6)/3-(-3))(e^-(-3)t-e^-3t)
Final Result
e^3t-e^-3t