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Consider a system of differential equations X Ax, where x = and the 2x2 matrix A has eigenpairs d1 = 3, 1 Vị = V2 1 V2 = and A2 = 2, %3D V2 From the options below, find the correct behavior of the solution x(t) = -Vị e^it + v2 edat. lim ||x(t)|| lim ||x(t)|| = 0, o, || t 00 x(t) x(t) lim lim x(0) V1, V2, t0 ||x(t)|| t-o ||x(t)|| lim ||x(t)|| = 0, lim ||x(t)|| =∞, t→∞ t -0 x(t) x(t) lim V1, lim = V2, x(0) t-0 ||x(t)|| t-o ||x(t)|| lim ||x(t)| lim ||x(t)|| = 0, = 0, x(t) x(0) = ,v. x(t) lim t-0 |x(t)|| lim V2, |3D V1, %3D t0 ||x(t)|| lim ||x(t)|| = 0, lim ||x(t)|| = ∞, t -0

Consider a system of differential equations X Ax, where x = and the 2x2 matrix A has eigenpairs d1 = 3, 1 Vị = V2 1 V2 = and A2 = 2, %3D V2 From the options below, find the correct behavior of the solution x(t) = -Vị e^it + v2 edat. lim ||x(t)|| lim ||x(t)|| = 0, o, || t 00 x(t) x(t) lim lim x(0) V1, V2, t0 ||x(t)|| t-o ||x(t)|| lim ||x(t)|| = 0, lim ||x(t)|| =∞, t→∞ t -0 x(t) x(t) lim V1, lim = V2, x(0) t-0 ||x(t)|| t-o ||x(t)|| lim ||x(t)| lim ||x(t)|| = 0, = 0, x(t) x(0) = ,v. x(t) lim t-0 |x(t)|| lim V2, |3D V1, %3D t0 ||x(t)|| lim ||x(t)|| = 0, lim ||x(t)|| = ∞, t -0

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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Consider a system of differential equations X'= Ax, where X = and the 2x2 matrix A has eigenpairs 1 Vị = 1 d1 = 3, and d2 = 2, V2 V2 From the options below, find the correct behavior of the solution x(t) = -Vị e^it + v2 est. lim ||x(t)|| lim ||x(t)|| = 0, = ∞, t→-∞ x(0) = [va): x(t) x(t) lim t→0 x(t)|| V1, lim V2, t-o ||x(t)|| lim ||x(t)|| = 0, lim ||x(t)|| =∞, t→∞ t -∞ x(t) x(t) lim x(0) V2, lim V1, 00 ||x(t)|| t-0 x(t)|| lim ||x(t)|| = ∞, lim ||x(t)|| = 0, t→∞ x(0) = ,v. x(t) x(t) lim t→-0 ||x(t)|| lim V1, V2, t>0 ||x(t)|| lim ||x(t)|| = 0, lim ||x(t)|| = 0∞, t→∞
Transcribed Image Text:Consider a system of differential equations X'= Ax, where X = and the 2x2 matrix A has eigenpairs 1 Vị = 1 d1 = 3, and d2 = 2, V2 V2 From the options below, find the correct behavior of the solution x(t) = -Vị e^it + v2 est. lim ||x(t)|| lim ||x(t)|| = 0, = ∞, t→-∞ x(0) = [va): x(t) x(t) lim t→0 x(t)|| V1, lim V2, t-o ||x(t)|| lim ||x(t)|| = 0, lim ||x(t)|| =∞, t→∞ t -∞ x(t) x(t) lim x(0) V2, lim V1, 00 ||x(t)|| t-0 x(t)|| lim ||x(t)|| = ∞, lim ||x(t)|| = 0, t→∞ x(0) = ,v. x(t) x(t) lim t→-0 ||x(t)|| lim V1, V2, t>0 ||x(t)|| lim ||x(t)|| = 0, lim ||x(t)|| = 0∞, t→∞
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