Determine the particular solution of the ODE below, where p and q are constants. [-]]]+[%][KO]-[] 2 3 (0) P (0) =
Determine the particular solution of the ODE below, where p and q are constants. [-]]]+[%][KO]-[] 2 3 (0) P (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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![Question 5
Determine the particular solution of the ODE below, where p and q are constants.
H-BA+K]-[]
0
a) eAt =
[1₂ (6)] = 64¹ [P] + √6 64(²-) [B(0)]ds
eAt
2
[7elt +2e-t 3e4t - 2e-t
2e4t+3et 2e4t - 3e-t
c) e4t = |
O a
[3et+2e-t
3e4t3e-t
b) eAt =
[1(0)]=e^t [P] + √6 e^(-) [B(0) de
So
ds
O b
2e-t 2e4t
3e-4e4t
[10]=64 [P]+√ e^(-) [E()]ds
eAt
d) et = |
O C
Od
2e4t - 2e-t
2e4t + 3e-t.
=
7
[7e4t +2e-t 3e4t - 2e-t
2e4t + 3e-t 2e4-3e-t
[120)] = 04² [1₂] + √6 e^(-0) [B(0)] ds
=e4t
(t
So](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F42dbffe9-6e96-44f7-b2da-dfd07848442a%2Fe863316b-bc5a-4aaf-91da-66e5d3324aa8%2Ff6s9vb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Question 5
Determine the particular solution of the ODE below, where p and q are constants.
H-BA+K]-[]
0
a) eAt =
[1₂ (6)] = 64¹ [P] + √6 64(²-) [B(0)]ds
eAt
2
[7elt +2e-t 3e4t - 2e-t
2e4t+3et 2e4t - 3e-t
c) e4t = |
O a
[3et+2e-t
3e4t3e-t
b) eAt =
[1(0)]=e^t [P] + √6 e^(-) [B(0) de
So
ds
O b
2e-t 2e4t
3e-4e4t
[10]=64 [P]+√ e^(-) [E()]ds
eAt
d) et = |
O C
Od
2e4t - 2e-t
2e4t + 3e-t.
=
7
[7e4t +2e-t 3e4t - 2e-t
2e4t + 3e-t 2e4-3e-t
[120)] = 04² [1₂] + √6 e^(-0) [B(0)] ds
=e4t
(t
So
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