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 → ∞

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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Question

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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