(a) Use appropriate algebra and Theorem to find the given inverse Laplace transform. (Write your answer as a function of t.) L−1 {3s − 10/ s2 + 25}
(b) Use the Laplace transform to solve the given initial-value problem.
y' + 3y = e6t, y(0) = 2

(a) Expand the given expression as

You should recognize the Laplace transform of sine and cosine:

So we have

(b) Take the Laplace transform of both sides:

Solve for :

Decompose the right side into partial fractions:

So we have

and taking the inverse transforms of both sides gives

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step-by-step explanation: