Question: The differential equation model for a particular chemical process has been found by testing to be as follows: where ? 1 and ? 2 are

The differential equation model for a particular chemical process has been found by testing to be as follows:

( +2)+ y Ku(t) d'y TIT2

where ?1 and ?2 are constant parameters and u(t) is the input function of time.

What are the functions of time (e.g., e?1) in the solution for each output y(t) for the following cases? (Optional: Find the solutions for y(t).)

(a) u(t) = aS(t)? ? ? ? ? ? ?unit step function

(b) u(t) = be?1/?? ? ? ? ? ? ? ? ?? ? ?1 ? ?2

(c) u(t) = ce?1/?? ? ? ? ? ? ? ? ?? ? ?1 ? ?2

(d) u(t) = d sin wt ? ? ???1 ? ?2

( +2)+ y Ku(t) d'y TIT2

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