Consider the initial value problem y' + 4y = (b) Solve your equation for Y. 0...

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Consider the initial value problem y' + 4y = (b) Solve your equation for Y. 0 12 0 if 0 < t <3 if 3 < t < 5 if 5 < t < ∞0, (a) Take the Laplace transform of both sides of the given differential equation to create the corresponding algebraic equation. Denote the Laplace transform of y by Y. Do not move any terms from one side of the equation to the other (until you get to part (b) below). y = Y = L {y} = (c) Take the inverse Laplace transform of both sides of the previous equation to solve for y. y(0) = 2. Consider the initial value problem y' + 4y = (b) Solve your equation for Y. 0 12 0 if 0 < t <3 if 3 < t < 5 if 5 < t < ∞0, (a) Take the Laplace transform of both sides of the given differential equation to create the corresponding algebraic equation. Denote the Laplace transform of y by Y. Do not move any terms from one side of the equation to the other (until you get to part (b) below). y = Y = L {y} = (c) Take the inverse Laplace transform of both sides of the previous equation to solve for y. y(0) = 2.