Laplace Transform: Example 1

Example 1: Solve using Laplace Transform

Answer: First, apply the Laplace Transform

Knowing that

,

and

we get

After easy algebraic manipulations we get

,

which implies

Next, we need to use the inverse Laplace.

We have (see the table)

For the second term we need to perform the partial decomposition technique first.

.

We get

Hence, we have

Since (see the table)

and (see the table)

Finally, we have