Find the solution of the given initial value problem. y" + y = g(t); y(0) = 5, y'(0) = 6; 0 6 O y(t) = (t – sin(t)) – u6(t)[(t – 6) – sin(t – 6)] + 5cos(t) + 6sin(t) 1 =(t – sin(t)) – 46(t)[(t – 6) – sin(t – 6)] + 5cos(f) + 6sin(t) y(t) - 2 1 2 1 y(t) = (t – sin(t)) + ¬u6(t)[(t – 6) – sin(t – 6)] + 5cos(t) + 6sin(t) - 1 y(1) = ¿(t – sin(t)) – ju6(1)[(t – 6) – sin(t – 6)] + 6cos(t) + 5sin(t) y(t) t – sin(t)) – u6(t)[(t – 6) – sin(t – 6)] + 5cos(t) + 6sin(t)
Find the solution of the given initial value problem. y" + y = g(t); y(0) = 5, y'(0) = 6; 0 6 O y(t) = (t – sin(t)) – u6(t)[(t – 6) – sin(t – 6)] + 5cos(t) + 6sin(t) 1 =(t – sin(t)) – 46(t)[(t – 6) – sin(t – 6)] + 5cos(f) + 6sin(t) y(t) - 2 1 2 1 y(t) = (t – sin(t)) + ¬u6(t)[(t – 6) – sin(t – 6)] + 5cos(t) + 6sin(t) - 1 y(1) = ¿(t – sin(t)) – ju6(1)[(t – 6) – sin(t – 6)] + 6cos(t) + 5sin(t) y(t) t – sin(t)) – u6(t)[(t – 6) – sin(t – 6)] + 5cos(t) + 6sin(t)
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
![Find the solution of the given initial value problem.
y" + y = g(t); y(0) = 5, y'(0) = 6;
0 <t < 6
g(t)
3, t> 6
O y(t) = (t – sin(t)) – u6(t)[(t – 6) – sin(t – 6)] + 5cos(t) + 6sin(t)
1
=(t – sin(t)) – 46(t)[(t – 6) – sin(t – 6)] + 5cos(f) + 6sin(t)
y(t)
-
2
1
2
1
y(t) = (t – sin(t)) + ¬u6(t)[(t – 6) – sin(t – 6)] + 5cos(t) + 6sin(t)
-
1
y(1) = ¿(t – sin(t)) – ju6(1)[(t – 6) – sin(t – 6)] + 6cos(t) + 5sin(t)
y(t)
t – sin(t)) – u6(t)[(t – 6) – sin(t – 6)] + 5cos(t) + 6sin(t)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc3394273-72c7-4098-9246-650448d9c593%2F02162ca0-3cc3-4f78-a9ae-a2d3dbffac61%2Fl315adn_processed.png&w=3840&q=75)
Transcribed Image Text:Find the solution of the given initial value problem.
y" + y = g(t); y(0) = 5, y'(0) = 6;
0 <t < 6
g(t)
3, t> 6
O y(t) = (t – sin(t)) – u6(t)[(t – 6) – sin(t – 6)] + 5cos(t) + 6sin(t)
1
=(t – sin(t)) – 46(t)[(t – 6) – sin(t – 6)] + 5cos(f) + 6sin(t)
y(t)
-
2
1
2
1
y(t) = (t – sin(t)) + ¬u6(t)[(t – 6) – sin(t – 6)] + 5cos(t) + 6sin(t)
-
1
y(1) = ¿(t – sin(t)) – ju6(1)[(t – 6) – sin(t – 6)] + 6cos(t) + 5sin(t)
y(t)
t – sin(t)) – u6(t)[(t – 6) – sin(t – 6)] + 5cos(t) + 6sin(t)
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