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Consider two tanks, A and B, each holding 200 litres of water. A pipe pumps water from tank A to tank B at a rate of 5l/min. At the same time another pipe pumps liquid from tank B to tank A at the same rate. At time t=0, kg of a chemical X is dissolved into tank A, and tank B has kg of the same chemical X dissolved into it.

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i). Write down the system of differential equations satisfied by x(t) and y(t), the quantity of the chemical X in tanks A and B respectively.

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ii). Find the eigenvalues and the eigenvectors of the resulting matrix form.

The eigenvalues are 0 and -2.

, Eigenvector:

, Eigenvector:

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iii). Show that the amount of the chemical X in either tank approaches as t approaches infinity.

At t=0:

Working this out gives:

as :

I get really far but this doesn't work out. It suggests that my inital formulae are wrong but I can't see where my mistake is. If I reversed my A and B my formulae would work, but I can't see how I can do this.

Help would be appreciated greatly!