Consider the following initial value problem: y (4) + 25y" + 144y = 1 − u(t); y(0) = 0, y'(0) = 0, y"(0) = 0, y" (0) = 0; (a) Sketch the graph of the forcing function on an appropriate interval. 1 y(t): st = 0.8 0.6 0.4 8 (b) Find the solution of the given initial value problem. NOTE: Denote the Heaviside function by uc(t) where uc (t) = 1 if t≥c and 0 otherwise. Indicate separately the value of c. 0.2 10 12

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