Suppose the same spring-mass system is now attached to a movable plank, which moves like the function 5 sin 2t for all t > 0. Adjust the initial value problem you wrote in part (a) to include this fact. Do not solve! 2. Find two linearly independent power series solutions of the differential equation (x + 2)y" + xy' – y = 0. 3. (а) Write the definition of the Laplace transform of a function f(t).

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