Use the method of variation of parameters to solve the initial value problem x' = Ax + f(t), x(a) = x₂ using the following values.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Use the method of variation of parameters to solve the initial value problem x' = Ax + f(t),
x(a)=x₂ using the following values.
17et
•[:]-[²]-[:]^{[
f(t) =
x(0) = eAt
32et
A =
3 1
4 2
0
0
=
1 4e²te-t-e²t + e-t
4e²t4e-t-e²t + 4e¯t
Transcribed Image Text:Use the method of variation of parameters to solve the initial value problem x' = Ax + f(t), x(a)=x₂ using the following values. 17et •[:]-[²]-[:]^{[ f(t) = x(0) = eAt 32et A = 3 1 4 2 0 0 = 1 4e²te-t-e²t + e-t 4e²t4e-t-e²t + 4e¯t
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