Consider the system of equations 10 -5 - (20 -10)x X 20 -10 x' = (a) Use a graphing utility to graph a direction field and a few trajectories. (b) Describe how the solutions behave as t→∞0. The equilibrium points lie on the line [Choose one ▾ Solutions starting at all other points x = Choose one Choose one x2 = -X1 x2 = -2x1 (c) Find the general solution of the syster 2 = 21-2 X2 = x1 x2 = 2x1 x2 = x1 + 2
Consider the system of equations 10 -5 - (20 -10)x X 20 -10 x' = (a) Use a graphing utility to graph a direction field and a few trajectories. (b) Describe how the solutions behave as t→∞0. The equilibrium points lie on the line [Choose one ▾ Solutions starting at all other points x = Choose one Choose one x2 = -X1 x2 = -2x1 (c) Find the general solution of the syster 2 = 21-2 X2 = x1 x2 = 2x1 x2 = x1 + 2
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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Same question both picture
Transcribed Image Text:Consider the system of equations
10
(20
x'
1)x
X
-5
20 -10
(a) Use a graphing utility to graph a direction field and a few
trajectories.
(b) Describe how the solutions behave as t → ∞.
The equilibrium points lie on the line [Choose one ▾
Solutions starting at all other points
X= Choose one ▼
(c) Find the general solution of the syster
Choose one
x2 = -X1
x2 = -2x1
x2 = x1-2
X2 = x1
= 2x1
x2 = 1 + 2
x2 =
![(a) Use a graphing utility to graph a direction field and a few
trajectories.
(b) Describe how the solutions behave as t→∞0.
The equilibrium points lie on the line Choose one
Solut
Choose one
(c) Pind (50)+[(5)+(9)]
10
X =
C1
a(1) + a[(1) + (-₁)]
et
te
C2
0
a(-1/2) + a[(-1/2)¹+ (2)]
t
C1
(1)¹+ 1
¹ + 0₂ [ ( 2₂ ) te ¹ + ( ₁ ) e +¹]
e
2
a()+ a[()+(-)]
t
2
2
7
ns.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F20c5837f-8a07-4fb0-b110-a8d2b8a51a74%2Fcc1dad24-543d-466d-af67-0bef92bdef2b%2Fxzmskdr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(a) Use a graphing utility to graph a direction field and a few
trajectories.
(b) Describe how the solutions behave as t→∞0.
The equilibrium points lie on the line Choose one
Solut
Choose one
(c) Pind (50)+[(5)+(9)]
10
X =
C1
a(1) + a[(1) + (-₁)]
et
te
C2
0
a(-1/2) + a[(-1/2)¹+ (2)]
t
C1
(1)¹+ 1
¹ + 0₂ [ ( 2₂ ) te ¹ + ( ₁ ) e +¹]
e
2
a()+ a[()+(-)]
t
2
2
7
ns.
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