a) Solve y" -6y' +9y=0. b) Find the particular solution of y"-6y' +9y=3-t c) Use the Laplace transform to solve the given initial value problem y"-6y' +9y=3-t, y(0)=0, y'(0) = 2

Q: 3y" + 6y + 3y = 9, y(0) = 0, /(0) = 6 %3D

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A: We shall use Laplace and inverse Laplace transform to solve this

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Q: D) y y(0) c) y" + 4y + 3y = 8(t-2), y(0) = 1, y'(0) = -1

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Q: 1) Using Laplace transform to solve: y" + 2y - 63y = 2, yco)=1, y'co)=0

A: Step 1: Step 2: Step 3: Step 4:Step 5:Step 6:

Q: y"+2ў-15y=0 усо)=1 y'(0)=-2

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Q: Determine the Fourier transform of the following signal: _(t+1) u(t+1) x (t) = è

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Q: 4 10 (2-A) 1 2 Jet O 5. Use Laplace transform to solve y' + y = e²x.

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Q: Can you solve in terms of thelaplace transform of Y(s) of the solution y(t)?

A: Please see the attached images for the solution.  If there are queries or if the images are not…