Example 1: Solve using Laplace Transform
Answer: First, apply the Laplace Transform
After easy algebraic manipulations we get
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.
Hence, we have
Since (see the table)
and (see the table)
Finally, we have
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Laplace Transform is utilized to calculate functions.