The amounts x,(t) and x2(t) of salt in two brine tanks satisfy the differential equations below, where k = r for i 1, 2. The volumes are V₁ = 20 (gal) and V₂ = 10 (gal). First solve for x, (t) and x2(t) assuming that r = 12 (gal/min), x,(0) = 3 (lb), and x2(0) = 0. Then construct a figure showing the graphs of x, (t) and x2(t). dx₁ dt dx2 dt -K₁x₁ + K2x2 = k₁x₁-k₂x2 x₁ (t)= X2(t)=
The amounts x,(t) and x2(t) of salt in two brine tanks satisfy the differential equations below, where k = r for i 1, 2. The volumes are V₁ = 20 (gal) and V₂ = 10 (gal). First solve for x, (t) and x2(t) assuming that r = 12 (gal/min), x,(0) = 3 (lb), and x2(0) = 0. Then construct a figure showing the graphs of x, (t) and x2(t). dx₁ dt dx2 dt -K₁x₁ + K2x2 = k₁x₁-k₂x2 x₁ (t)= 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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Transcribed Image Text:The amounts x,(t) and x2(t) of salt in two brine tanks satisfy the differential
equations below, where k =
r
for i 1, 2. The volumes are V₁ = 20 (gal)
and V₂ = 10 (gal). First solve for x, (t) and x2(t) assuming that r = 12
(gal/min), x,(0) = 3 (lb), and x2(0) = 0. Then construct a figure showing the
graphs of x, (t) and x2(t).
dx₁
dt
dx2
dt
-K₁x₁ + K2x2 = k₁x₁-k₂x2
x₁ (t)=
X2(t)=
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