Consider the integro-differential equation dy + 4| dt [ relt-r)dr y(T)dr + 4y(t) = subject to | y(T)dt = 1 and y(0) = 0. (a) Find Y(s), the Laplace transform of y(t). (b) Use your result from part (a) to express y(t) in the form y(t) = A+ Bf1(t) + C f2(t) + Df3(t). Note: you do not need to find the real constants A, B,C, D.

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