æ' = 2) 4e x + %3D -4 3 2e er the associated homogeneous system
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
![Consider the nonhomogeneous system:
2.
x +
3.
1
(4et
x' =
4
2et
a. Write a fundamental matrix for the associated homogeneous system
X =
b. Compute the inverse of X.
X-1 =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8c8c30dd-8618-4d51-9f32-993bb170f9da%2F4001585a-7b8d-4c65-9aa4-8e60d5f096f8%2Fzwjo6q_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider the nonhomogeneous system:
2.
x +
3.
1
(4et
x' =
4
2et
a. Write a fundamental matrix for the associated homogeneous system
X =
b. Compute the inverse of X.
X-1 =
![X-1 -
c. Multiply by the nonhomogenity g(t) and integrate.
C1
u(t) = | x-'(t)g(t) dt =
C2
d. Write the general solution to the system.
+ C2
æ(t)
C1
%3D](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8c8c30dd-8618-4d51-9f32-993bb170f9da%2F4001585a-7b8d-4c65-9aa4-8e60d5f096f8%2Fucx5v2k_processed.jpeg&w=3840&q=75)
Transcribed Image Text:X-1 -
c. Multiply by the nonhomogenity g(t) and integrate.
C1
u(t) = | x-'(t)g(t) dt =
C2
d. Write the general solution to the system.
+ C2
æ(t)
C1
%3D
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