I have attached a picture of the whole assignment

I need with question a. I have attached a picture of the whole assignment. Transcribed Image Text: Consider the start value problem for t > 0:
y” (t) – 6y'(t) + 13y(t) = -8e²”,
y(0) = 0, y'(0) = 10.
Y(s) = Ly(s).
a) Determine the image equation for the Laplace transformed function
(Hint: Use
on both sides of the differential equation.)
that originates from y(0)
b) Indicate the inverse Laplace transformed of the joints in
to y'(0).
s2 – 6s + 13 = (s – 3)² + 4.)
(Hint: you can show and use that
c) Determine the solution y(t)


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