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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, (t) 0 (b) у" — 0, Ф(t) — t (c) y"4y 0, (t)0 (d) y"4y 0, (t) = cos2t (e) y"4y4y 0, ¢(t)0 (f) y"4y4y 0, <(t) = e-2t (g) y" 4y0, ¢(t) 0 (h) y" — 4у — 0, Ф(() — е- 2

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, (t) 0 (b) у" — 0, Ф(t) — t (c) y"4y 0, (t)0 (d) y"4y 0, (t) = cos2t (e) y"4y4y 0, ¢(t)0 (f) y"4y4y 0, <(t) = e-2t (g) y" 4y0, ¢(t) 0 (h) y" — 4у — 0, Ф(() — е- 2

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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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, (t) 0 (b) у" — 0, Ф(t) — t (c) y"4y 0, (t)0 (d) y"4y 0, (t) = cos2t (e) y"4y4y 0, ¢(t)0 (f) y"4y4y 0, <(t) = e-2t (g) y" 4y0, ¢(t) 0 (h) y" — 4у — 0, Ф(() — е- 2
Transcribed Image Text: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, (t) 0 (b) у" — 0, Ф(t) — t (c) y"4y 0, (t)0 (d) y"4y 0, (t) = cos2t (e) y"4y4y 0, ¢(t)0 (f) y"4y4y 0, <(t) = e-2t (g) y" 4y0, ¢(t) 0 (h) y" — 4у — 0, Ф(() — е- 2
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