olve the initial value problem. Find the solution of the given initial value problem. Determine the behavior of th y" + 12y' = 0, y(0) = -8, y'(0) = 12 Oy=7+e-12¹, limy(t) = 7 Oy = −7+e-¹21, limy(t) = -7 1-00 Oy=7-e-12¹, Oy=-7-e-121, O y = 7+e¹2¹, limy(t) = ∞ limy(t) = 7 limy(t) = -7

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Solve the initial value problem. Find the solution of the given initial value problem. Determine the behavior of the solution as t → *.
y" +12y = 0, y(0) = -8, y'(0) = 12
Oy = 7+e-12, limy(t) = 7
1-→00
Oy
Oy = 7-e-¹²¹, limy(t) = 7
1-00
- 7+e-12t, limy(t) = -7
1-→00
Oy = 7e-12t, limy(t) = -7
1-00
O y = 7+ e¹2t, limy(t) = ∞
1-00
Transcribed Image Text:Solve the initial value problem. Find the solution of the given initial value problem. Determine the behavior of the solution as t → *. y" +12y = 0, y(0) = -8, y'(0) = 12 Oy = 7+e-12, limy(t) = 7 1-→00 Oy Oy = 7-e-¹²¹, limy(t) = 7 1-00 - 7+e-12t, limy(t) = -7 1-→00 Oy = 7e-12t, limy(t) = -7 1-00 O y = 7+ e¹2t, limy(t) = ∞ 1-00
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