The system of mixing tanks shown in Figure 8.2.7 is a closed system. The tanks A, B, and C initially contain the number of gallons of brine indicated in the figure. Figure 8.2.7 Mixing tanks mixture 5 gal/min A B C 100 gal 100 gal 50 gal mixture mixture 5 gal/min 5 gal/min (a) Construct a mathematical model in the form of a linear system of first- order differential equations for the number of pounds of salt æ1 (t), x2(t) and æ3 (t) in the tanks A, B, and C at time t, respectively. 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) = 30, x2(0) = 20, x3(0) = 5.
The system of mixing tanks shown in Figure 8.2.7 is a closed system. The tanks A, B, and C initially contain the number of gallons of brine indicated in the figure. Figure 8.2.7 Mixing tanks mixture 5 gal/min A B C 100 gal 100 gal 50 gal mixture mixture 5 gal/min 5 gal/min (a) Construct a mathematical model in the form of a linear system of first- order differential equations for the number of pounds of salt æ1 (t), x2(t) and æ3 (t) in the tanks A, B, and C at time t, respectively. 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) = 30, x2(0) = 20, x3(0) = 5.
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:The system of mixing tanks shown in Figure 8.2.7 is a closed system. The
tanks A, B, and C initially contain the number of gallons of brine indicated in
the figure.
Figure 8.2.7
Mixing tanks
mixture
5 gal/min
A
B
C
100 gal
100 gal
50 gal
mixture
mixture
5 gal/min
5 gal/min
(a) Construct a mathematical model in the form of a linear system of first-
order differential equations for the number of pounds of salt ¤1 (t), x2(t)
and æ3 (t) in the tanks A, B, and C at time t, respectively. Write the system
in matrix form.
(b) Use the eigenvalue method of this section to solve the linear system in
part (a) subject to x1(0) = 30, x2(0) = 20, x3(0) = 5.
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