x" + 4x = S(t) + S(t-π) x(0)=0, x'(0)=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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x" + 4x = S(t) + S(t = π) x(0)=0, x'(0)=0
a. x(t)= =sin(2t)
x(t) = 1/([1-e²
е
b.
c.
d.
e.
-21-2te-²¹] + µ(t− 2)(t− 2)e-2 (1-21)
x(t)=2u(t)e-(-)sin(t - π)
x(t)=[2-e²Tu(t− π) + e¹¹µ(t − 2π)]e-²¹ sint
x(t) = ½ [1 + µ(t-
-[1+µ(t− n)]sin(2t)
Transcribed Image Text:x" + 4x = S(t) + S(t = π) x(0)=0, x'(0)=0 a. x(t)= =sin(2t) x(t) = 1/([1-e² е b. c. d. e. -21-2te-²¹] + µ(t− 2)(t− 2)e-2 (1-21) x(t)=2u(t)e-(-)sin(t - π) x(t)=[2-e²Tu(t− π) + e¹¹µ(t − 2π)]e-²¹ sint x(t) = ½ [1 + µ(t- -[1+µ(t− n)]sin(2t)
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