1. Perform the required integrations to get the result in the notes e2t dr et dr že [00 (tt) Bu(t)dt = [_e-² [² ["²e²¹d²] -e-21 e²t dt +2e-4t et dr (2e-2t-e-41) Þ(1)x(0): [₁ (-4e-21 +4e-41) Find the following result, and write the equations for x₁ (t) and x₂ (t) seperately x(1) = Þ(1)x(0) + [* Þ(1 − 1)Bu(t)dr 2. Given that =

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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1. Perform the required integrations to get the result in
the notes
-41
[ e² dr - 12 e 4 fe²
et dr
že
["(t = T) Bu(r)dt =
-
-e-² f²e²² dr +2e=41
2e-4 f et dr
2. Given that
(2e-21-e-41)
(1)x(0) =
-4e-2t + 4e¯
Find the following result, and write the equations for
x₁ (t) and x₂ (t) seperately
x(t) = Þ(t)x(0) +
So
(tr)Bu(r)dr
Transcribed Image Text:1. Perform the required integrations to get the result in the notes -41 [ e² dr - 12 e 4 fe² et dr že ["(t = T) Bu(r)dt = - -e-² f²e²² dr +2e=41 2e-4 f et dr 2. Given that (2e-21-e-41) (1)x(0) = -4e-2t + 4e¯ Find the following result, and write the equations for x₁ (t) and x₂ (t) seperately x(t) = Þ(t)x(0) + So (tr)Bu(r)dr
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