Find the solution of the given initial value problem. y" + y = g(t); y(0) = 2, y'(0) = 6; Si 0
Find the solution of the given initial value problem. y" + y = g(t); y(0) = 2, y'(0) = 6; Si 0
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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![Find the solution of the given initial value problem.
y" +y = g(t); y(0) = 2, y'(0) = 6;
, 0<1<6
g(t) =
3, t2 6
1
y(t) = (t – sin(t)) +
s(t)[(t – 6) – sin(t – 6)] + 2cos(t) + 6sin(t)
y(1) =
1
(t – sin(t))
1
– u6 (t)[(t – 6) – sin(t – 6)] + 6cos(t) + 2sin(t)
O y(t) = (t – sin(t)) – u6(t)[(t – 6) – sin(t – 6)] + 2cos(t) + 6sin(t)
1
y(t) =
(t – sin(t)) – u6(1)[(t – 6) – sin(t - 6)] + 2cos(t) + 6sin(t)
y(t)
-(t – sin(t)) – u6(t)[(t – 6) – sin(t – 6)] + 2cos(t) + 6sin(t)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F22838496-0258-4d5c-876c-e3e418ae27cb%2F98d61714-42e8-41b9-a8b2-34d806fd9c8a%2Fmdr6527_processed.png&w=3840&q=75)
Transcribed Image Text:Find the solution of the given initial value problem.
y" +y = g(t); y(0) = 2, y'(0) = 6;
, 0<1<6
g(t) =
3, t2 6
1
y(t) = (t – sin(t)) +
s(t)[(t – 6) – sin(t – 6)] + 2cos(t) + 6sin(t)
y(1) =
1
(t – sin(t))
1
– u6 (t)[(t – 6) – sin(t – 6)] + 6cos(t) + 2sin(t)
O y(t) = (t – sin(t)) – u6(t)[(t – 6) – sin(t – 6)] + 2cos(t) + 6sin(t)
1
y(t) =
(t – sin(t)) – u6(1)[(t – 6) – sin(t - 6)] + 2cos(t) + 6sin(t)
y(t)
-(t – sin(t)) – u6(t)[(t – 6) – sin(t – 6)] + 2cos(t) + 6sin(t)
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