(Solved): Differential Equation: Laplace Translation Theorems 1. (12) Three tanks are filled with a dye solut ...

Expert Answer

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Given data:

Three tanks are filled with a dye solution. Tanks   and   initially contains   hg of dye and tank   is initially pure water. A solution that contains   of dye is pumped into tank   at a rate of    The solution in tank   flows out to tank   at a rate of   and out an exhaust spout at a rate of   . The solution in tank    flows into tank    at a rate of   , into tank   at a rate of   , and out an exhaust spout at a rate of   


To find:

Set up a system to determine the amount of dye in each tank at a given time   .
Write your final system in matrix form. 

Now,

Let    denote the amounts (in hg) of dye in tanks   and   , respectively.
Both    and    start with   of dye, so   .
   starts off containing only pure water, so