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-12 8 A = 8. (a) Write down the general solution of the system = Aã. %3D (b) Say whether or not we have lim 7(t) = 0 for the general solution 7(t) you found in (a) (meaning: %3D 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 7." Say what i is, and explain briefly. (d) Find the unique solution with initial condition a(0) = %3D

-12 8 A = 8. (a) Write down the general solution of the system = Aã. %3D (b) Say whether or not we have lim 7(t) = 0 for the general solution 7(t) you found in (a) (meaning: %3D 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 7." Say what i is, and explain briefly. (d) Find the unique solution with initial condition a(0) = %3D

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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-12 8 | А — (a) Write down the general solution of the system d = Aã. dt (b) Say whether or not we have lim (t) = 0 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 d." Say what ở is, and explain briefly. (d) Find the unique solution with initial condition 7(0) 3
Transcribed Image Text:-12 8 | А — (a) Write down the general solution of the system d = Aã. dt (b) Say whether or not we have lim (t) = 0 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 d." Say what ở is, and explain briefly. (d) Find the unique solution with initial condition 7(0) 3
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