Consider the two tanks shown in the figure below. Assume that tank A contains 50 gallons of water in
which 25 pounds of salt is dissolved. Suppose tank B contains 50 gallons of pure water. Liquid is pumped
into and out of the tanks as indicated in the figure; the mixture exchanged between the two tanks and the
liquid pumped out of tank B are assumed to be well stirred. We wish to construct a mathematical model
that describes the number of pounds
Solutions:
(1)
This system is described by the system of equations
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x1(0) = 25,with
x2(0) = 0
initial conditions
(2)
dy1
x
x
 4* 2  16 * 1 ,
dt
200
200
dx2
x1
x
 16*
 16* 2
dt
200
200
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