du Consider a differential equation = p(u), where p(u) has the graph shown in dt 3. Fig. 1. (a) At what values of u does this differential equation have equilibrium points? (b) Sketch the phase line for this differential equation. |p(u) 4 2 - -6.5 0.5 1.0 -2 -4 Figure 1: Plot of p(u) used in que 3. (c) For each interval bounded by equilibrium points, describe the long term behaviour of solutions which start in this interval. Make sure you consider the cases t o and t → -0. (d) Thus, sketch the phase line and describe the long-term behaviour of solutions of the differential equation dk 100(k – 1)(k – 0.5)k²(k +0.5). db
du Consider a differential equation = p(u), where p(u) has the graph shown in dt 3. Fig. 1. (a) At what values of u does this differential equation have equilibrium points? (b) Sketch the phase line for this differential equation. |p(u) 4 2 - -6.5 0.5 1.0 -2 -4 Figure 1: Plot of p(u) used in que 3. (c) For each interval bounded by equilibrium points, describe the long term behaviour of solutions which start in this interval. Make sure you consider the cases t o and t → -0. (d) Thus, sketch the phase line and describe the long-term behaviour of solutions of the differential equation dk 100(k – 1)(k – 0.5)k²(k +0.5). db
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:du
Consider a differential equation
= p(u), where p(u) has the graph shown in
dt
3.
Fig. 1.
(a) At what values of u does this differential equation have equilibrium points?
(b) Sketch the phase line for this differential equation.
|p(u)
4
2 -
-6.5
0.5
1.0
-2
-4
Figure 1: Plot of p(u) used in que
3.
(c) For each interval bounded by equilibrium points, describe the long term behaviour of
solutions which start in this interval. Make sure you consider the cases t → o and
t → -00.
(d) Thus, sketch the phase line and describe the long-term behaviour of solutions of the
differential equation
dk
100(k – 1)(k – 0.5)k² (k + 0.5).
db
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