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1. Find real-valued fundamental solutions of the differential equation 1 x' = Ax, A= 2 %3D 4 -3

1. Find real-valued fundamental solutions of the differential equation 1 x' = Ax, A= 2 %3D 4 -3

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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1. Find real-valued fundamental solutions of the differential equation 2 x' = Ax, A = 4. %3D 3 2. Find the solution of the initial value problem x' = Ax, x(0) = 3. Classify (for example, source node, sink node. etc) the solution X = 0. 4. Sketch a phase portrait of the solution to the initial value problem found in part (2). • Label your axes with the components of x = • Indicate the direction of increasing time for the solution drawn. • Mark the regions of t > 0, of t < 0, and the point in the solution at t = 0.
Transcribed Image Text:1. Find real-valued fundamental solutions of the differential equation 2 x' = Ax, A = 4. %3D 3 2. Find the solution of the initial value problem x' = Ax, x(0) = 3. Classify (for example, source node, sink node. etc) the solution X = 0. 4. Sketch a phase portrait of the solution to the initial value problem found in part (2). • Label your axes with the components of x = • Indicate the direction of increasing time for the solution drawn. • Mark the regions of t > 0, of t < 0, and the point in the solution at t = 0.
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