You are given the following system: dạy 3u(t) = dt2 +5 dy + 6y dt Remember that u(t) is the unit step function, meaning:

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You are given the following system: dạy 3u(t) = dt2 +5 dy + 6y dt Remember that u(t) is the unit step function, meaning: = t < 0 t20 u(t) = {0; Determine the complete solution y(t) = y(t) + yp(t). You are told that y(0) = 0 and y'(O) = 1. a) Determine the steady-state solution yp(t). b) Determine the two values of s that determine the transient solution, y(t).

c) Write y(t) and y'(t) in terms of the two unknowns C and C2 d) Determine the two unknowns C and C2 and provide a final expression for y(t)