9. För each of the following equations, decide the solution given is asymptotically stable, stable but not asymptotically stable, or unstable. (a) y" = 0, 4(t) = 0. (c) y"+ 4y = 0, $(t) = 0. (e) y" + 4y' +4y =0, 6(t) = 0. (g) y" – 4y = 0, $(t) = 0. (b) y" = 0, 6(t) =t. (d) y" + 4y = 0, $(t) = cos 2t. (f) y" + 4y' + 4y 0, 6(t) = e-2". (h) y" – 4y = 0, $(t) = e-2". %3D
9. För each of the following equations, decide the solution given is asymptotically stable, stable but not asymptotically stable, or unstable. (a) y" = 0, 4(t) = 0. (c) y"+ 4y = 0, $(t) = 0. (e) y" + 4y' +4y =0, 6(t) = 0. (g) y" – 4y = 0, $(t) = 0. (b) y" = 0, 6(t) =t. (d) y" + 4y = 0, $(t) = cos 2t. (f) y" + 4y' + 4y 0, 6(t) = e-2". (h) y" – 4y = 0, $(t) = e-2". %3D
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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
Transcribed Image Text:9. For each of the following scalar differential equations, decide whether the
solution given is asymptotically stable, stable but not asymptotically stable, or
unstable.
(a) y" = 0, 4(t) = 0.
(c) y" + 4y = 0, $(t) = 0.
(e) y" + 4y' + 4y =0, (t) = 0.
(3) у" — 4у 3D 0, Ф() %3D 0.
(b) y" = 0, 4(t)=t.
(d) у" + 4у %3D 0, Ф(г) — сos 2r.
(f) y" + 4y' +4y = 0, 6(t) = e-2".
(h) у" — 4у - 0, Ф() — е-21,
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