Question

Consider the initial value problem y" + 9y = cos(3t), y(0) = 8, y'(0) = 2. 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(t) by Y(s). Do not move any terms from one side of the equation to the other

Answer 1

To obtain the Laplace transform, we write the given differential equation as: s^2Y(s) + 9Y(s) = 1/(s^2 + 9). Where Y(s) represents the Laplace transform of y(t). We can now solve this algebraic equation to find Y(s).

Step-by-step explanation:

To obtain the Laplace transform, we write the given differential equation as:

s^2Y(s) + 9Y(s) = 1/(s^2 + 9)

Where Y(s) represents the Laplace transform of y(t). We can now solve this algebraic equation to find Y(s).