Solve the equation y"+y=f(t), y(0)= 0, y'(0) = 1 0
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.CR: Chapter 11 Review
Problem 13CR
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![Solve the equation y" + y = f(t), y(0) = 0, y'(0) = 1
1 0<t<π/2
0
where f(t) =
F(s) =
π/2≤t<∞
a. y(t)=1-cost + sint -u(t - π/2)(1-sint)
b. y(t) = cost+u(t- π/2)(1-sint(t - π/2)
c. y(t)= 1-sint +-u(t-1/2)(1-cos(t - π/2)
d.
y(t) = sint -cost-u(t - n/2)(1-sin(t - π/2) + cos(t - π/2))
Oa
O b
O C
1-e-(π/2)s
S
Od](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5fce1f36-3621-4521-9495-ef38f12af896%2F62c4a865-3f5d-4eeb-8942-79088c21cfe1%2Fghffpw_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Solve the equation y" + y = f(t), y(0) = 0, y'(0) = 1
1 0<t<π/2
0
where f(t) =
F(s) =
π/2≤t<∞
a. y(t)=1-cost + sint -u(t - π/2)(1-sint)
b. y(t) = cost+u(t- π/2)(1-sint(t - π/2)
c. y(t)= 1-sint +-u(t-1/2)(1-cos(t - π/2)
d.
y(t) = sint -cost-u(t - n/2)(1-sin(t - π/2) + cos(t - π/2))
Oa
O b
O C
1-e-(π/2)s
S
Od
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