Question

Find the inverse Laplace transform of (5s/(s-2)²).

a) (5e²t)
b) (5te²t)
c) (5te⁻2t)
d) (5e⁻2t)

Answer 1

The inverse Laplace transform of (5s/(s-2)²) is (5e^(2t) - 10t e^(2t)).

Step-by-step explanation:

To find the inverse Laplace transform of (5s/(s-2)²), we can use the following steps:

1. First, we will decompose the given expression into partial fractions. The expression can be written as 5/(s-2) - 10/(s-2)².
2. Next, we can use the following Laplace Transform pairs:
   • L^-1{1/(s-a)} = e^(at)
   • L^-1{(n!/(s-a)^(n+1))} = t^n e^(at)
3. Applying these pairs, we get the inverse Laplace transform of 5/(s-2) as 5e^(2t).
4. Similarly, we can find the inverse Laplace transform of -10/(s-2)² as -10t e^(2t).
5. Combining both results, we get the inverse Laplace transform of (5s/(s-2)²) as (5e^(2t) - 10t e^(2t)).