Question: Use the Laplace transform to solve the following initial value problem: y - 8y' + 12y = 0, y(0) = -8, y'(0) = 4 (1)

Use the Laplace transform to solve the following initial value problem: y" - 8y' + 12y = 0, y(0) = -8, y'(0) = 4 (1) First, using Y for the Laplace transform of y(t), i.e., Y = [(y(t)), find the equation you get by taking the Laplace transform of the differential equation to obtain Y(s)(s-2)(s-6)+8s-68 = 0 (2) Next solve for Y = (68-8s)/((S-2)(s-6)) A B (3) Now write the above answer in its partial fraction form, Y = S a S (NOTE: the order that you enter your answers matter so you must order your terms so that the first corresponds to a and the second to b, where a

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