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2. Consider the IVP: y'' + 4y = 6(t 3), y(0) = 4, y' (0) = 0. (a) Solve this IVP using the Laplace Transforms.
2. Consider the IVP: y'' + 4y = 6(t 3), y(0) = 4, y' (0) = 0.
(a) Solve this IVP using the Laplace Transforms. Write the solution as a piecewise-defined function.
(b) For t > 3, find A, , and so that your solution is of the form: y(t) = A sin(t + ).
(c) Graph your solution. What happens graphically at t = 3?
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