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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