. As shown in Figure 8.2.6 two large connected mixing tanks A and B initially contain 100 gallons of brine. Liquid is pumped in and out of the tanks as indicated in the figure; the mixture pumped between and out of a tank is assumed to be well-stirred. Figure 8.2.6 Mixing tanks pure water mixture 2 gal/min 1 gal/min B mixture mixture mixture I gal/min 2 gal/min I gal/min (a) Construct a mathematical model in the form of a linear system of first- order differential equations for the number of pounds ¤1 (t) and #2 (t) of salt in tanks A and B, respectively, at time t. Write the system in matrix form. (b) Use the eigenvalue method of this section to solve the linear system in part (a) subject to ¤1(0) = 20, æ2(0) = 5. (c) Use a graphing utility or CAS to plot the graphs of ¤1 (t) and æ2(t) in the same coordinate plane.
. As shown in Figure 8.2.6 two large connected mixing tanks A and B initially contain 100 gallons of brine. Liquid is pumped in and out of the tanks as indicated in the figure; the mixture pumped between and out of a tank is assumed to be well-stirred. Figure 8.2.6 Mixing tanks pure water mixture 2 gal/min 1 gal/min B mixture mixture mixture I gal/min 2 gal/min I gal/min (a) Construct a mathematical model in the form of a linear system of first- order differential equations for the number of pounds ¤1 (t) and #2 (t) of salt in tanks A and B, respectively, at time t. Write the system in matrix form. (b) Use the eigenvalue method of this section to solve the linear system in part (a) subject to ¤1(0) = 20, æ2(0) = 5. (c) Use a graphing utility or CAS to plot the graphs of ¤1 (t) and æ2(t) in the same coordinate plane.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Solve the exercise in the image, by using
Transcribed Image Text:. As shown in Figure 8.2.6 two large connected mixing tanks A and B initially
contain 100 gallons of brine. Liquid is pumped in and out of the tanks as
indicated in the figure; the mixture pumped between and out of a tank is
assumed to be well-stirred.
Figure 8.2.6
Mixing tanks
pure water
mixture
2 gal/min
1 gal/min
A
B
mixture
1 gal/min
mixture
mixture
2 gal/min
1 gal/min
(a) Construct a mathematical model in the form of a linear system of first-
order differential equations for the number of pounds ¤1(t) and x2 (t) of salt
in tanks A and B, respectively, at time t. Write the system in matrix form.
(b) Use the eigenvalue method of this section to solve the linear system in
part (a) subject to ¤1 (0) = 20, æ2 (0) = 5.
(c) Use a graphing utility or CAS to plot the graphs of ¤1 (t) and #2(t) in the
same coordinate plane.
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