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Find constant 3x 1 vectors u and uz such that the solution of the initial value problem 2 -4 -3 x' = 3 -5 -3 x, x(0) = x0 -2 2 1 tends to (0,0,0)" as t → o for any xo € S, where S = { u: u = a¡u¡ + azu2, - 0 < a1, az < o} Describe the behavior of solutions as t → o if xo E S. uj = 0 Jand u2 = 0. uj = 1 and u2 = uj = o Jand uz = uj = 1 Jand u2 = If xo ¢ S, then x(t) approaches as → o the line determined by the vector

Find constant 3x 1 vectors u and uz such that the solution of the initial value problem 2 -4 -3 x' = 3 -5 -3 x, x(0) = x0 -2 2 1 tends to (0,0,0)" as t → o for any xo € S, where S = { u: u = a¡u¡ + azu2, - 0 < a1, az < o} Describe the behavior of solutions as t → o if xo E S. uj = 0 Jand u2 = 0. uj = 1 and u2 = uj = o Jand uz = uj = 1 Jand u2 = If xo ¢ S, then x(t) approaches as → o the line determined by the vector

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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Find constant 3x1 vectors u and u2 such that the solution of the initial value problem 2 -4 -3 x' = 3 -5 -3 x, x(0) = x. -2 2 1 tends to (0,0,0)" as t → o for any xo € S, where S = {u: u = a¡u¡ + ażu2, - o < a1, az < ∞} Describe the behavior of solutions as t → oif xo £ S. uj = 0 Jand u2 = uj = 1 Jand u2 = uj = o Jand u2 = uj = 1 and u2 = If xo ¢ S, then x(t) approaches as → o the line determined by the vector
Transcribed Image Text:Find constant 3x1 vectors u and u2 such that the solution of the initial value problem 2 -4 -3 x' = 3 -5 -3 x, x(0) = x. -2 2 1 tends to (0,0,0)" as t → o for any xo € S, where S = {u: u = a¡u¡ + ażu2, - o < a1, az < ∞} Describe the behavior of solutions as t → oif xo £ S. uj = 0 Jand u2 = uj = 1 Jand u2 = uj = o Jand u2 = uj = 1 and u2 = If xo ¢ S, then x(t) approaches as → o the line determined by the vector
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