QUESTION 3. Consider the differential equation r' = Ax, (1) where -3 1 :) A= -3 1 -1 a) Find the fundamental solution matrix X(t) of (1) that satisfies X (0) = I, where I is the 3 x 3 identity matrix. b) Find the solution of the differential equation a' (t) = Ax + (1 where r(0) = c) Discuss the stability of the origin of the homogeneous equation a' Ar.

QUESTION 3. Consider the differential equation r' = Ax, (1) where -3 1 :) A= -3 1 -1 a) Find the fundamental solution matrix X(t) of (1) that satisfies X (0) = I, where I is the 3 x 3 identity matrix. b) Find the solution of the differential equation a' (t) = Ax + (1 where r(0) = c) Discuss the stability of the origin of the homogeneous equation a' Ar.

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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Differential Equations

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