Use the method of variation of parameters to solve the initial value problem x' = Ax + f(t), x(a)=x₂ using the following values. --E-D-S [:] x(0) = eAt = x(t) = 5 2 |, f(t) = 15e2t 35e2t 3t 2t 18- 8887 18 + 5e³t - e-t-e³t + è¯ 5e³t 5e-t-e³t + 5e¯t
Use the method of variation of parameters to solve the initial value problem x' = Ax + f(t), x(a)=x₂ using the following values. --E-D-S [:] x(0) = eAt = x(t) = 5 2 |, f(t) = 15e2t 35e2t 3t 2t 18- 8887 18 + 5e³t - e-t-e³t + è¯ 5e³t 5e-t-e³t + 5e¯t
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter3: The Derivative
Section3.CR: Chapter 3 Review
Problem 59CR
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Question
![Use the method of variation of parameters to solve the initial value problem x' = Ax + f(t),
x(a) = x₂ using the following values.
[HD|HS|
[:]
x(0) =
eAt
x(t) =
=
5 - 2
|, f(t) =
15e2t
35e2t
3t
2t
-8-8-81
+
5e³t - e-t - e³t + 鲯
5e³t 5e-t-e³t + 5e¯t](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3200e892-7b83-4670-8aa5-c4c84f2a6adb%2F2c74599e-6054-4324-b774-8ea8cebe035d%2Fpkibvzh_processed.png&w=3840&q=75)
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.
[HD|HS|
[:]
x(0) =
eAt
x(t) =
=
5 - 2
|, f(t) =
15e2t
35e2t
3t
2t
-8-8-81
+
5e³t - e-t - e³t + 鲯
5e³t 5e-t-e³t + 5e¯t
Expert Solution
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Step 1: Write the IVP
VIEWStep 2: Determine the eigenvalues of A and the eigenvectors corresponding to the eigenvalues
VIEWStep 3: Determine the complementary function
VIEWStep 4: Use the method of variation of parameters
VIEWStep 5: Determine the particular solution
VIEWStep 6: Determine the required solution of the given IVP
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