d²y dy dy + 2 + 6y = 0 y(0) = 2, (0) = a > 0. dt dt2 dt (a) Find the solution y(t) of this problem (b)Find a so that y = 0 whent =1 (c) Find, as a function of a, the smaller positive value of t for which y = 0 d) Determine the limit of the expression found in part (c) as a → ∞. %3D

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Deffrional equation, help with only branch, C and D

Q2: Consider the initial value problem.
d²y
dy
+ 2-+ 6y = 0
dt
dy
(0) = a > 0.
dt
y(0) = 2,
dt²
(a) Find the solution y(t) of this problem
(b)Find a so that y = 0 when t =1
(c) Find, as a function of a, the smaller positive value of t for which y = 0
(d) Determine the limit of the expression found in part (c) as a → ∞.
Transcribed Image Text:Q2: Consider the initial value problem. d²y dy + 2-+ 6y = 0 dt dy (0) = a > 0. dt y(0) = 2, dt² (a) Find the solution y(t) of this problem (b)Find a so that y = 0 when t =1 (c) Find, as a function of a, the smaller positive value of t for which y = 0 (d) Determine the limit of the expression found in part (c) as a → ∞.
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