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1. Given the system X x = ( 3 4 3): X (a) Write the general solution. Hint: See Worksheet 11. (b) Classify the critical (equilibrium) point (0,0). (c) Sketch the phase portrait. Make sure you include the straight-line (eigendirection) solutions and at least two other trajectories. 2. Given the system dx = -5x-2y dt dy = -x-4y dt (a) Write the general solution. Hint: See Worksheet 11. (b) Classify the critical (equilibrium) point (0,0). (c) Sketch the phase portrait. Make sure you include the straight-line (eigendirection) solutions and at least two other trajectories.

1. Given the system X x = ( 3 4 3): X (a) Write the general solution. Hint: See Worksheet 11. (b) Classify the critical (equilibrium) point (0,0). (c) Sketch the phase portrait. Make sure you include the straight-line (eigendirection) solutions and at least two other trajectories. 2. Given the system dx = -5x-2y dt dy = -x-4y dt (a) Write the general solution. Hint: See Worksheet 11. (b) Classify the critical (equilibrium) point (0,0). (c) Sketch the phase portrait. Make sure you include the straight-line (eigendirection) solutions and at least two other trajectories.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 17EQ
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1. Given the system X x = ( 3 4 3): X (a) Write the general solution. Hint: See Worksheet 11. (b) Classify the critical (equilibrium) point (0,0). (c) Sketch the phase portrait. Make sure you include the straight-line (eigendirection) solutions and at least two other trajectories. 2. Given the system dx = -5x-2y dt dy = -x-4y dt (a) Write the general solution. Hint: See Worksheet 11. (b) Classify the critical (equilibrium) point (0,0). (c) Sketch the phase portrait. Make sure you include the straight-line (eigendirection) solutions and at least two other trajectories.
Transcribed Image Text:1. Given the system X x = ( 3 4 3): X (a) Write the general solution. Hint: See Worksheet 11. (b) Classify the critical (equilibrium) point (0,0). (c) Sketch the phase portrait. Make sure you include the straight-line (eigendirection) solutions and at least two other trajectories. 2. Given the system dx = -5x-2y dt dy = -x-4y dt (a) Write the general solution. Hint: See Worksheet 11. (b) Classify the critical (equilibrium) point (0,0). (c) Sketch the phase portrait. Make sure you include the straight-line (eigendirection) solutions and at least two other trajectories.
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