Question

Compute L ⁻¹{ 3s² e⁻ˢ +2／s²}.

Answer 1

To compute L⁻¹{3s² e⁻ˢ +2／s²}, we need to use the inverse Laplace transform. We can break down the expression into two parts: 3s² e⁻ˢ and 2／s².

Step-by-step explanation:

To compute L-1{3s² e-s +2/s²}, we need to use the inverse Laplace transform. We can break down the expression into two parts: 3s² e-s and 2/s².

For the first part, 3s² e-s, we can use the Laplace transform property: L{t^n eat}= n!/(s-a)^(n+1). Here, n = 2 and a = -1. So, the Laplace transform of 3s² e-s is 3!/(s-(-1))^(2+1) = 6/(s+1)³.

For the second part, 2/s², we can use the Laplace transform property: L{t^(-n)} = n!/(s)^(n+1). Here, n = 2. So, the Laplace transform of 2/s² is 2!/s^(2+1) = 2/s³.

Now, we add the two Laplace transforms together: L-1{3s² e-s +2/s²} = L-1{6/(s+1)³ + 2/s³}.