t x(t) be the solution of the initial value problem S 8 sint ift <1 if t > * ' + 4x' + 5x = ere t > 0 and r(0) =r'(0) = 0. Write the RHS of the DE using the Heaviside function. 1-р p² +1 S (e-24 + 1) sint + (e-2ª – 1) cost ift *
t x(t) be the solution of the initial value problem S 8 sint ift <1 if t > * ' + 4x' + 5x = ere t > 0 and r(0) =r'(0) = 0. Write the RHS of the DE using the Heaviside function. 1-р p² +1 S (e-24 + 1) sint + (e-2ª – 1) cost ift *
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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![Let x(t) be the solution of the initial value problem
2" + 4x' + 5x =Į 8sint ift <.
if t >n'
where t >0 and x(0) = x'(0) = 0.
(a) Write the RHS of the DE using the Heaviside function.
(b) Hence show that L[x(t)] = (1+
(1+e¯P*)
1-p
+
p+3
p² +1
(e-2t + 1) sint + (e-2t – 1) cos t if t<a
e-"(1 – e2")(sin t+ cos t)
(p+2)² +1
(c) Hence show that r(t)
if t >7](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff258f736-2efe-4abc-a546-b1bd73d984a7%2F19f360e7-9255-47dd-b9db-91b8d44c8cdf%2Ft583qac_processed.png&w=3840&q=75)
Transcribed Image Text:Let x(t) be the solution of the initial value problem
2" + 4x' + 5x =Į 8sint ift <.
if t >n'
where t >0 and x(0) = x'(0) = 0.
(a) Write the RHS of the DE using the Heaviside function.
(b) Hence show that L[x(t)] = (1+
(1+e¯P*)
1-p
+
p+3
p² +1
(e-2t + 1) sint + (e-2t – 1) cos t if t<a
e-"(1 – e2")(sin t+ cos t)
(p+2)² +1
(c) Hence show that r(t)
if t >7
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