[40] (a) Solve y"(t)+9y(t) = f(t), y(0) = 0, y'(0) = -1, where f(t) Express the answer using the symbols of unit step functions. (b) Express the answer obtained in (a) piecewisely. 0 9t 0 0 2π.
[40] (a) Solve y"(t)+9y(t) = f(t), y(0) = 0, y'(0) = -1, where f(t) Express the answer using the symbols of unit step functions. (b) Express the answer obtained in (a) piecewisely. 0 9t 0 0 2π.
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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Question
40 work is provided by instructor for practice, not graded
![[40] (a) Solve y"(t)+9y(t) = f(t), y(0) = 0, y'(0) = -1, where f(t)
Express the answer using the symbols of unit step functions.
(b) Express the answer obtained in (a) piecewisely.
[40] (a) y(t) =
(b) y(t) =
0
9t
0
0<t<π,
π < t < 2π,
t> 2π.
-
sin(3t)+u(t−ñ) [t+ sin(3t) + π cos(3t)] −u(t−2ñ) [t − ½ sin(3t) — 2π cos(3t)]
-sin(3t)
t<π,
t + π cos(3t)
π < t < 2π,
sin (3t) + 3 cos (3t)
t> 2π.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8c89c353-252e-4eca-b673-064be33ffdb0%2Fa109ab72-4a34-4784-8869-8477db816576%2Fz5dst6_processed.png&w=3840&q=75)
Transcribed Image Text:[40] (a) Solve y"(t)+9y(t) = f(t), y(0) = 0, y'(0) = -1, where f(t)
Express the answer using the symbols of unit step functions.
(b) Express the answer obtained in (a) piecewisely.
[40] (a) y(t) =
(b) y(t) =
0
9t
0
0<t<π,
π < t < 2π,
t> 2π.
-
sin(3t)+u(t−ñ) [t+ sin(3t) + π cos(3t)] −u(t−2ñ) [t − ½ sin(3t) — 2π cos(3t)]
-sin(3t)
t<π,
t + π cos(3t)
π < t < 2π,
sin (3t) + 3 cos (3t)
t> 2π.
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