Consider the initial value problem y" + 25y = cos(5t), y(0) = 6, 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 (until you get to part (b) below). (formulas) b. Solve your equation for Y(s). Y(s) = L{y(t)} = = y(t) = = c. Take the inverse Laplace transform of both sides of the previous equation to solve for y(t). = help

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