Let A be the matrix A₂ = -1 and corresponding eigenvectors are v₁ = - V2 = - H Let x(t) be the position of a particle at time t that satisfies the initial value problem x' = Ax, x(0) : x = 4x, x(0) = [14] C₁ = 1 -2 3-4 If the unique solution is x(t) = [2(t)] = a[1] e C1 emt C2 whose eigenvalues are λ₁ = -2, 2 [3] m= n = + C₂ 2 3 and ent e" then
Let A be the matrix A₂ = -1 and corresponding eigenvectors are v₁ = - V2 = - H Let x(t) be the position of a particle at time t that satisfies the initial value problem x' = Ax, x(0) : x = 4x, x(0) = [14] C₁ = 1 -2 3-4 If the unique solution is x(t) = [2(t)] = a[1] e C1 emt C2 whose eigenvalues are λ₁ = -2, 2 [3] m= n = + C₂ 2 3 and ent e" then
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
![H
Let A be the matrix
3
A₂ = -1 and corresponding eigenvectors are v₁ =
V2 =
H
Let x(t) be the position of a particle at time t that satisfies the
initial
value problem x' = Ax, x(0) =
If the unique solution is
x(t) = [22 (8)]
[20]=[]
=C1
C1
C2
IF
m=
whose eigenvalues are >₁ = -2,
[3]
n=
Q Search
emt
14
+C₂
2
[3]
ON
ent
and
then](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F018dde93-f85e-4b68-97c4-7858fe4b7f30%2F7a418251-10c4-41ea-bc2d-91658ff99311%2Foxo2po_processed.jpeg&w=3840&q=75)
Transcribed Image Text:H
Let A be the matrix
3
A₂ = -1 and corresponding eigenvectors are v₁ =
V2 =
H
Let x(t) be the position of a particle at time t that satisfies the
initial
value problem x' = Ax, x(0) =
If the unique solution is
x(t) = [22 (8)]
[20]=[]
=C1
C1
C2
IF
m=
whose eigenvalues are >₁ = -2,
[3]
n=
Q Search
emt
14
+C₂
2
[3]
ON
ent
and
then
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