The amounts x₁ (t) and x2(t) of salt in two brine tanks satisfy the differential equations below, where k₁ = for i = 1, 2. The volumes are V₁ = 50 (gal) and V₂ = 25 (gal). First solve for x₁ (t) and x2(t) assuming that r = 30 (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). dx1 dt = dx2 -=k₁x₁-K2x2 dt x₁ (t)= X2(t)=
The amounts x₁ (t) and x2(t) of salt in two brine tanks satisfy the differential equations below, where k₁ = for i = 1, 2. The volumes are V₁ = 50 (gal) and V₂ = 25 (gal). First solve for x₁ (t) and x2(t) assuming that r = 30 (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). dx1 dt = dx2 -=k₁x₁-K2x2 dt 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 x₁ (t) and x2(t) of salt in two brine tanks satisfy the differential
equations below, where k₁ =
for i = 1, 2. The volumes are V₁ = 50 (gal) and
V₂ = 25 (gal). First solve for x₁ (t) and x2(t) assuming that r = 30 (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).
dx1
dt
=
dx2
-=k₁x₁-K2x2
dt
x₁ (t)=
X2(t)=
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