3. Consider the system of first order ODEs (in matrix form) 5 x': = -(₁3)× (a) Show that (*)-(1) * *-( :-)"} x(²) (t) = = = 7 t- is a set of fundament al solutions of the system, for all real numbers t. (b) What type of equilibrium solution does this system have? Is the equilibrium solution asymptotically stable, neutrally stable or unstable? I (c) Determine the fundamental matrix (t) which satisfies Þ(0) = -(1) 01

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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3. Consider the system of first order ODES (in matrix form)
x-(::).
3
(a) Show that
t -
x® (t) =
t –
(t) =
et
4t
- 2
is a set of fund ame nt al solutions of the system, for all real numbers t.
(b) What type of equilibrium solution does this system have? Is the equilibrium solution
as ymptotically stable, neutrally stable or unst able?
(c) Determine the fundamental matrix (t) which satisfies (0) =
1 0
%3D
01
Transcribed Image Text:3. Consider the system of first order ODES (in matrix form) x-(::). 3 (a) Show that t - x® (t) = t – (t) = et 4t - 2 is a set of fund ame nt al solutions of the system, for all real numbers t. (b) What type of equilibrium solution does this system have? Is the equilibrium solution as ymptotically stable, neutrally stable or unst able? (c) Determine the fundamental matrix (t) which satisfies (0) = 1 0 %3D 01
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