Consider the following initial value problem: Edi y(4) + 41y" + 400y = 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 0.8 0.6 0.4 0.2 10 12 (b) Find the solution of the given initial value problem. NOTE: Denote the Heaviside function by uc(t) where uelt) = 1 if t > c and 0 otherwise. Indicate separately the value of c. y(t) =

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A: Step 1: Step 2: Step 3: Step 4:

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Q: Find y as a function of x if y(0)=29, y'(0) = 16, y"(0) = 20. y(x)= = y" — 11y" + 18y' = 32e,

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