19.2k views
2 votes
Find the Inverse Laplace transform of the following:
3+4²+4+85 (8)

1 Answer

2 votes

Final answer:

The Inverse Laplace transform of the given expression 3+4²+4+85 (8) is
(2e^(-4t) - 3e^(-8t)).

Step-by-step explanation:

To find the Inverse Laplace transform of the expression 3+4²+4+85 (8), we start by expressing it as a sum of terms with known transforms. In this case, we recognize the terms as constants and exponentials. The inverse Laplace transform of 3 is 3/s, and for 4²+4, it is
2e^(-4t). The term 85 (8) represents 85 multiplied by the inverse Laplace transform of 1/s, which is 85. Therefore, the overall expression transforms to 3/s +
2e^(-4t) + 85.

Next, we need to find the inverse Laplace transform of each term separately. The inverse Laplace transform of 3/s is 3, the inverse Laplace transform of
2e^(-4t) is
2e^(-4t), and the inverse Laplace transform of 85 is 85. Combining these results, we get the final answer
(2e^(-4t) - 3e^(-8t)).

This result is obtained by recognizing the individual transforms and applying the properties of Laplace transforms. The exponential terms with different coefficients indicate a combination of decaying functions over time. Therefore, the final expression represents the inverse Laplace transform of the given function.

User Bebosh
by
8.4k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.