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Suppose that the differential equation x' = Ax is such that A is a 2 x 2 matrix with eigenvalues A1 = 5 and X2 = 3 and corresponding eigenvectors vị = and v2 = Plot the phase portrait. Include in your plot the trajectories of the associated fundamental solutions. Label trajectories and indicate the direction that the points move along the trajectory as t → ∞. Then highlight the trajectory of this system that passes through the point (2,0) indicating the behavior of this trajectory as t → ∞

Suppose that the differential equation x' = Ax is such that A is a 2 x 2 matrix with eigenvalues A1 = 5 and X2 = 3 and corresponding eigenvectors vị = and v2 = Plot the phase portrait. Include in your plot the trajectories of the associated fundamental solutions. Label trajectories and indicate the direction that the points move along the trajectory as t → ∞. Then highlight the trajectory of this system that passes through the point (2,0) indicating the behavior of this trajectory as t → ∞

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.CR: Chapter 11 Review
Problem 12CR
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Suppose that the differential equation x' = Ax is such that A is a 2 x 2 matrix with eigenvalues A1 = 5 and A2 = 3 and corresponding eigenvectors v = and v2 = Plot the phase portrait. Include in your plot the trajectories of the associated fundamental solutions. Label trajectories and indicate the direction that the points move along the trajectory as t → o. Then highlight the trajectory of this system that passes through the point (2,0) indicating the behavior of this trajectory as t → ∞
Transcribed Image Text:Suppose that the differential equation x' = Ax is such that A is a 2 x 2 matrix with eigenvalues A1 = 5 and A2 = 3 and corresponding eigenvectors v = and v2 = Plot the phase portrait. Include in your plot the trajectories of the associated fundamental solutions. Label trajectories and indicate the direction that the points move along the trajectory as t → o. Then highlight the trajectory of this system that passes through the point (2,0) indicating the behavior of this trajectory as t → ∞
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