Applied Analysis

Solve the systems of linear equations z '= Az. If no initial condition is given,
find the general solution .

3. This is an interconnected pollution problem. Suppose we have a two tan
system subject to
1. Tank 1 initially contains 30 liters of water and 25g of salt. Tank
initially contains 20 l of water and 15 g of salt.
2. Water from outside containing 1g/l of salt follows into Tank 1 at a rat
of 1.5 l/min. Solution drains to Tank 2 at a rate of 3 l/min.
3. Water containing 3 g/l of salt flow into Tank 2 at a rate of 1 l/mi
from the outside.
4. The mixture drains from Tank 2 at a rate of 4 l/min. Of this, 1.5 l/mi
goes to tank 1 and the rest drains away.

Show this leads to a system of equations

Now show the equilibrium solution is

If we let show that

and solve the initial value problem .

Answers