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Answer:
Please read the complete procedure below:
Step-by-step explanation:
You have the following initial value problem:
a) The algebraic equation obtain by using the Laplace transform is:
next, you replace (1) and (2):
(this is the algebraic equation)
b)
(this is the solution for Y(s))
c)
To find the inverse Laplace transform of the first term you use partial fractions:
Thus, you have:
(this is the solution to the differential equation)