[13] For each of the following equations, find general solutions; solve the initial value problem with initial condition x₁ (0) = -1, x₂ (0) = 2; • sketch the phase portrait, identify the type of each equilibrium, and determine the stability of each equilibrium. d +4x₂ -5 0 (a) (18]-[45] OE-736] *-[72] = (b) (c) x' X dt X2 +5x₂ 4 X2 0
[13] For each of the following equations, find general solutions; solve the initial value problem with initial condition x₁ (0) = -1, x₂ (0) = 2; • sketch the phase portrait, identify the type of each equilibrium, and determine the stability of each equilibrium. d +4x₂ -5 0 (a) (18]-[45] OE-736] *-[72] = (b) (c) x' X dt X2 +5x₂ 4 X2 0
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
![[13] For each of the following equations,
find general solutions;
• solve the initial value problem with initial condition x₁(0) = -1, x₂ (0) = 2;
• sketch the phase portrait, identify the type of each equilibrium, and determine the
stability of each equilibrium.
x₁ +4x₂
-5
0
(a) =[ 1
d x1
dt X2
() =
»E]-[73][B] ©*-[72]*
(c)
=
4
-x1 + 5x₂
-
X2
0](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F691b7a67-6813-4d00-98c8-39eebcbbc486%2Fdb5940c1-5c66-495a-8538-5ecac41d72e3%2Fpcpl92_processed.png&w=3840&q=75)
Transcribed Image Text:[13] For each of the following equations,
find general solutions;
• solve the initial value problem with initial condition x₁(0) = -1, x₂ (0) = 2;
• sketch the phase portrait, identify the type of each equilibrium, and determine the
stability of each equilibrium.
x₁ +4x₂
-5
0
(a) =[ 1
d x1
dt X2
() =
»E]-[73][B] ©*-[72]*
(c)
=
4
-x1 + 5x₂
-
X2
0
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