Unformatted text preview: 28 1 Solutions Integrating and simplifying gives
. The initial condition
implies
so
. Now the
brine solution in Tank 1 has concentration
and ﬂows into Tank 2 at a rate of liters per minute. Thus
L
g
input rate for Tank 2: input rate
min
L
g
.
min
L
g
g
output rate for Tank 2: output rate
.
min
L
min
The initial value problem for Tank 2 is thus: Simplifying and putting this equation in standard form gives The integrating factor is again (as for the Tank 1 equation)
Thus multiplying by the integrating factor gives . Integrating and simplifying gives The initial condition implies so 33. Let
and
denote the amount of salt in
respectively, at time . The volume of ﬂuid at time
and Tank 2 is
.
L
input rate for Tank 1: input rate
min
output rate for Tank 1: output rate Tank 1 and Tank 2,
in Tank 1 is
g
L
L
min g
.
min g
. The initial value problem for Tank 1 is thus
min Simplifying this equation and putting it in standard form gives g
L ...
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 Fall '08
 BELL,D
 Boundary value problem, Tank

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