13. -1 X(t) = [1¹3]X(t), X(0) = -3
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
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13
![In the following problems, find the general solution, find a particular solution corresponding to the
given initial data, and plot the phase portrait:
4.
6.
{X(t) = [₁5] X(t), _X (0) =
=
dt
1
X(0)=2x). X(0)=
10. X(t) = 13 X(t), X(0) = [2]
dt
8.
12.
X() = X(), X(0) =
dt
dt
-H
X=[5]X(),
d.
dt X (t)
X(t), X(0) = 2
.
5.
9.
7.
11.
d
X(t) = [¹, 2] X(t), X(0)
dt
-1
d
dt
13.
-X(t)
=
d
ẳx = [ổ ]x),
dt
=
d
dt X (t)
1
[X(),
1X(t), X(0) =
-1
X(t), X(0) = 2
d
X(t) = [2] X(t), X(0) = [1]
dt
= [13] x(), X(0) =
(2)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F71886d56-a83a-4d7b-8e18-9a0e9bdd4c82%2Fa7e5aa0b-af51-4e0b-a9e4-2e2900f28e04%2Felbso3_processed.jpeg&w=3840&q=75)
Transcribed Image Text:In the following problems, find the general solution, find a particular solution corresponding to the
given initial data, and plot the phase portrait:
4.
6.
{X(t) = [₁5] X(t), _X (0) =
=
dt
1
X(0)=2x). X(0)=
10. X(t) = 13 X(t), X(0) = [2]
dt
8.
12.
X() = X(), X(0) =
dt
dt
-H
X=[5]X(),
d.
dt X (t)
X(t), X(0) = 2
.
5.
9.
7.
11.
d
X(t) = [¹, 2] X(t), X(0)
dt
-1
d
dt
13.
-X(t)
=
d
ẳx = [ổ ]x),
dt
=
d
dt X (t)
1
[X(),
1X(t), X(0) =
-1
X(t), X(0) = 2
d
X(t) = [2] X(t), X(0) = [1]
dt
= [13] x(), X(0) =
(2)
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