Consider a system of differential equations which has the general solution: 18]- = C, · cos (5. t) – sin (5 - t) )+C2 · sin (5 - t) + • Cos (5 - t (a) Determine the fundamental matrix (t) which has the property (0) = I. (t) = (b) Use the fundamental matrix found in part (a) to quickly determine the particular solution for the following initial conditions: 미:8]-[3] r (t) : y (t) = (0): 1 (ii) -1 r (t) = y (t) =
Consider a system of differential equations which has the general solution: 18]- = C, · cos (5. t) – sin (5 - t) )+C2 · sin (5 - t) + • Cos (5 - t (a) Determine the fundamental matrix (t) which has the property (0) = I. (t) = (b) Use the fundamental matrix found in part (a) to quickly determine the particular solution for the following initial conditions: 미:8]-[3] r (t) : y (t) = (0): 1 (ii) -1 r (t) = y (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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![Consider a system of differential equations which has the general solution:
18]-
= C,
· cos (5. t) –
sin (5 - t) )+C2
· sin (5 - t) +
• Cos (5 - t
(a) Determine the fundamental matrix (t) which has the property (0) = I.
(t) =
(b) Use the fundamental matrix found in part (a) to quickly determine the particular solution for the following initial conditions:
r (t) :
y (t) =
:8]-[-
(0):
1
(ii)
r (t) =
y (t) =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F857b9df5-c991-4b19-87f3-b52c04b7240b%2Ff083658d-f76c-4235-823f-221ac27ead23%2Foin5at_processed.png&w=3840&q=75)
Transcribed Image Text:Consider a system of differential equations which has the general solution:
18]-
= C,
· cos (5. t) –
sin (5 - t) )+C2
· sin (5 - t) +
• Cos (5 - t
(a) Determine the fundamental matrix (t) which has the property (0) = I.
(t) =
(b) Use the fundamental matrix found in part (a) to quickly determine the particular solution for the following initial conditions:
r (t) :
y (t) =
:8]-[-
(0):
1
(ii)
r (t) =
y (t) =
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