For each of the systems in Questions (1) to (5) below, do the following: Draw the phase diagram of the system; list all the equilibrium points; determine the stability of the equilibrium points; and describe the outcome of the system from various initial points. You should consider all four quadrants of the xy-plane. (For full marks, all the following must be included, correct and clearly annotated in your phase diagram: The coordinate axes; all the isoclines; all the equilibrium points; the allowed directions of motion (both vertical and horizontal) in all the regions into which the isoclines divide the xy plane; direction of motion along isoclines, where applicable; examples of allowed trajectories in all regions and examples of trajectories crossing from a region to another, whenever such a crossing is possible. Please note that only hand-drawn phase diagrams will be marked and the use of online phase diagram plotter is prohibited.) Question (1.1) Question 2: (2.1) Question 3: (3.1) Question 4: (4.1) Question 5: (5.1) -xy.x-7. (x-y)(x+y).--y. -7(x2-x). -7(y²-y). -(x+y). (y-1)(xy-y). dx=-x, = (xy2 - xy - y² + y).

For each of the systems in Questions (1) to (5) below, do the following: Draw the phase diagram of the system; list all the equilibrium points; determine the stability of the equilibrium points; and describe the outcome of the system from various initial points. You should consider all four quadrants of the xy-plane. (For full marks, all the following must be included, correct and clearly annotated in your phase diagram: The coordinate axes; all the isoclines; all the equilibrium points; the allowed directions of motion (both vertical and horizontal) in all the regions into which the isoclines divide the xy plane; direction of motion along isoclines, where applicable; examples of allowed trajectories in all regions and examples of trajectories crossing from a region to another, whenever such a crossing is possible. Please note that only hand-drawn phase diagrams will be marked and the use of online phase diagram plotter is prohibited.) Question (1.1) Question 2: (2.1) Question 3: (3.1) Question 4: (4.1) Question 5: (5.1) -xy.x-7. (x-y)(x+y).--y. -7(x2-x). -7(y²-y). -(x+y). (y-1)(xy-y). dx=-x, = (xy2 - xy - y² + y).

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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