(d) Sketch the graphs of solutions. (e) Find the formula for the general solution.
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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Topic Video
Question
Q46(d) and (e)
![45. Let x(t) be the amount of time between two consecutive trolley cars as described
above. We claim that a reasonable model for x (t) is
dx
Вх — а.
%3D
dt
Which term represents the rate of decrease of the time between the trains if no people
are waiting, and which term represents the effect of the people waiting for the second
train? (Justify your answer.) Should the parameters a and B be positive or negative?
rder Differential Equations
46. For the model in Exercise 45:
(a) Find the equilibrium points.
(b) Classify the equilibrium points (source, sink, or node).
(c) Sketch the phase line.
(d) Sketch the graphs of solutions.
(e) Find the formula for the general solution.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F11c79b17-eda1-4727-979c-2308ac3d1e89%2F7ec2abdb-a8af-4e56-950e-c6d8be1323b7%2Fzw98ccc_processed.png&w=3840&q=75)
Transcribed Image Text:45. Let x(t) be the amount of time between two consecutive trolley cars as described
above. We claim that a reasonable model for x (t) is
dx
Вх — а.
%3D
dt
Which term represents the rate of decrease of the time between the trains if no people
are waiting, and which term represents the effect of the people waiting for the second
train? (Justify your answer.) Should the parameters a and B be positive or negative?
rder Differential Equations
46. For the model in Exercise 45:
(a) Find the equilibrium points.
(b) Classify the equilibrium points (source, sink, or node).
(c) Sketch the phase line.
(d) Sketch the graphs of solutions.
(e) Find the formula for the general solution.
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