# Laplace Transform

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

http://webpages.dcu.ie/~applebyj/ms224/BT2_LAP.pdf

http://www.sosmath.com/diffeq/laplace/basic/basic.html

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#### Solution Summary

Laplace Transform is utilized to calculate functions.