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Consider the system dx = x + 2y dt dx = -y dt and its corresponding direction field. (a) Sketch a number of different solution curves on the phase plane. 3.0 2.0 1.0 0.0 -1.0 -2.0 -3.0 -4 -3 -2 -1 1 2 3 4 (b) Describe the behavior of the solution that satisfies the initial condition (xo, yo) = (-2,2). (You can use software and try a number of initial conditions like (–1, 1),(-2,2) and (-3, 3). Observe and think why? )

Consider the system dx = x + 2y dt dx = -y dt and its corresponding direction field. (a) Sketch a number of different solution curves on the phase plane. 3.0 2.0 1.0 0.0 -1.0 -2.0 -3.0 -4 -3 -2 -1 1 2 3 4 (b) Describe the behavior of the solution that satisfies the initial condition (xo, yo) = (-2,2). (You can use software and try a number of initial conditions like (–1, 1),(-2,2) and (-3, 3). Observe and think why? )

Advanced Engineering Mathematics
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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2. Consider the system dx = x + 2y dt dx -y dt and its corresponding direction field. (a) Sketch a number of different solution curves on the phase plane. 3.0 2.0 1.0 0.0 -1.0 -2.0 -3.0 -4 -3 -2 -1 2 3 (b) De (You can use software and try a number of initial conditions like (-1, 1),(-2, 2) and (-3, 3). Observe and think why? ) ribe the behavior of the solution the satisfies the initial condition (xo, yo) (-2, 2). = II
Transcribed Image Text:2. Consider the system dx = x + 2y dt dx -y dt and its corresponding direction field. (a) Sketch a number of different solution curves on the phase plane. 3.0 2.0 1.0 0.0 -1.0 -2.0 -3.0 -4 -3 -2 -1 2 3 (b) De (You can use software and try a number of initial conditions like (-1, 1),(-2, 2) and (-3, 3). Observe and think why? ) ribe the behavior of the solution the satisfies the initial condition (xo, yo) (-2, 2). = II
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