[5 A -1 3 1 (a) Write down the general solution of the system da = Aã. (b) Say whether or not we have lim (t) t 00 O for the general solution (t) you found in (a) (meaning for all possible initial conditions), and explain briefly. (c) Consider the statement "As t grows without bound, the solution (t) will be mostly along th span of the vector 7." Say what ở is, and explain briefly. (d) Find the unique solution with initial condition (0) =
[5 A -1 3 1 (a) Write down the general solution of the system da = Aã. (b) Say whether or not we have lim (t) t 00 O for the general solution (t) you found in (a) (meaning for all possible initial conditions), and explain briefly. (c) Consider the statement "As t grows without bound, the solution (t) will be mostly along th span of the vector 7." Say what ở is, and explain briefly. (d) Find the unique solution with initial condition (0) =
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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A =
1
(a) Write down the general solution of the system = A.
dt
(b) Say whether or not we have lim 7(t) = Ở for the general solution 7(t) you found in (a) (meaning:
for all possible initial conditions), and explain briefly.
(c) Consider the statement “As t grows without bound, the solution (t) will be mostly along the
span of the vector J." Say what ở is, and explain briefly.
(d) Find the unique solution with initial condition 7(0) = |
3
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