Question
Asked Nov 17, 2019
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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
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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

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Consider the given scalar differential equation Here, the solutions of (a), (c), (e) and (g) are asymptotically stable. Because d(t)0 as t-»o Since asymptotically stable implies that stable Consider the case (b) then ø(t) -»o. When Thus, the solution is unstable. Consider the case (d) )=lcos 2r <1 then ø(t) -»1 When Thus, the solution is stable Consider the case (f) 1 =

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