Find the particular solution of the system dx1 dt Зx1 + X3, dx2 dt 9х1 — х2 + 2х з, dx3 = -9x1 + 4x2 - X3 dt that satisfies the initial conditions x1(0) = 0, x2(0) = 0, x3(0) = 17. The amounts x1 (t) and x2(t) of salt in the two brine tanks of Fig. 5.2.7 satisfy the differential equations dx1 = -k1x1, dt dx2 = k1x1 – k2x2, dt where k; = r/V; for i = 1, 2. In Problems 27 and 28 the vol- umes V1 and V½ are given. First solve for x1(t) and x2(t), as- suming that r = 10 (gal/min), x1 (0) = 15 (lb), and x2(0) = 0. Then find the maximum amount of salt ever in tank 2. Finally, construct a figure showing the graphs of x1(t) and x2(t).
Find the particular solution of the system dx1 dt Зx1 + X3, dx2 dt 9х1 — х2 + 2х з, dx3 = -9x1 + 4x2 - X3 dt that satisfies the initial conditions x1(0) = 0, x2(0) = 0, x3(0) = 17. The amounts x1 (t) and x2(t) of salt in the two brine tanks of Fig. 5.2.7 satisfy the differential equations dx1 = -k1x1, dt dx2 = k1x1 – k2x2, dt where k; = r/V; for i = 1, 2. In Problems 27 and 28 the vol- umes V1 and V½ are given. First solve for x1(t) and x2(t), as- suming that r = 10 (gal/min), x1 (0) = 15 (lb), and x2(0) = 0. Then find the maximum amount of salt ever in tank 2. Finally, construct a figure showing the graphs of x1(t) and x2(t).
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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Find the particular solution of the system Mentioned in the Attachment.
Transcribed Image Text:Find the particular solution of the system
dx1
dt
Зx1
+ X3,
dx2
dt
9х1 — х2 + 2х з,
dx3
= -9x1 + 4x2 - X3
dt
that satisfies the initial conditions x1(0) = 0, x2(0) = 0,
x3(0) = 17.
The amounts x1 (t) and x2(t) of salt in the two brine tanks of
Fig. 5.2.7 satisfy the differential equations
dx1
= -k1x1,
dt
dx2
= k1x1 – k2x2,
dt
where k; = r/V; for i = 1, 2. In Problems 27 and 28 the vol-
umes V1 and V½ are given. First solve for x1(t) and x2(t), as-
suming that r = 10 (gal/min), x1 (0) = 15 (lb), and x2(0) = 0.
Then find the maximum amount of salt ever in tank 2. Finally,
construct a figure showing the graphs of x1(t) and x2(t).
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