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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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 =
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
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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