Inverse Laplace transform of 5/(s - 2)

Step by step, with the reason for every step · The inverse Laplace transform · Differential Equations

Step by step

Question: find the inverse Laplace transform of 5/(s − 2).

ℒ⁻¹{5s − 2} =

The inverse transform goes back: which function of t has this transform?

We read the table backwards.

ℒ⁻¹: back from s to t

Each piece is already a row of the table.

e^(at) → 1s − a

Careful!

s − 2 means a = 2: the opposite sign of the number in the bracket.

Careful: not 5/(s − 2) → e^(−2t) ✗

Read the table backwards, piece by piece: 5e^(2t).

f(t) = 5e^(2t)

Let's check: the table forwards turns our answer back into 5/(s − 2).

Right!

forwards: 5e^(2t) → 5s − 2

Let's look back.

First: use the table backwards.

Last: check.

Answer

f(t) = 5e^(2t)

Try this one yourself, then check:

ℒ⁻¹{10s − 2}

Show the answer

f(t) = 10e^(2t)