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Use the variation of parameters formula to find a general solution of the system x'(t) = Ax(t) + f(t), where A and f(t) are given. A = - 16 4 4 -1 f(t)= 7+4t_1 ( Let x(t) = x₁(t) + xp (t), where x₁ (t) is the general solution corresponding to the homogeneous system, and xp (t) is a particular solution to the nonhomogeneous system. Find x₁ (t) and x (t).

Use the variation of parameters formula to find a general solution of the system x'(t) = Ax(t) + f(t), where A and f(t) are given. A = - 16 4 4 -1 f(t)= 7+4t_1 ( Let x(t) = x₁(t) + xp (t), where x₁ (t) is the general solution corresponding to the homogeneous system, and xp (t) is a particular solution to the nonhomogeneous system. Find x₁ (t) and x (t).

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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K Use the variation of parameters formula to find a general solution of the system x'(t) = Ax(t) + f(t), where A and f(t) are given. A = - 16 4 -1 f(t) = 7+4t. Let x(t) = x₁ (t) + xp (t), where x₁ (t) is the general solution corresponding to the homogeneous system, and xp (t) is a particular solution to the nonhomogeneous system. Find x₁ (t) and xp (t). Xp Xh(t) = 1 xp (t) = 9 (Type your answer as a single matrix.)
Transcribed Image Text:K Use the variation of parameters formula to find a general solution of the system x'(t) = Ax(t) + f(t), where A and f(t) are given. A = - 16 4 -1 f(t) = 7+4t. Let x(t) = x₁ (t) + xp (t), where x₁ (t) is the general solution corresponding to the homogeneous system, and xp (t) is a particular solution to the nonhomogeneous system. Find x₁ (t) and xp (t). Xp Xh(t) = 1 xp (t) = 9 (Type your answer as a single matrix.)
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