Solve the initial value problem with [3] Classify the nature of the origin as an attractor, repeller, or saddle point of the dynamical system described Ax-b. Find the directions of greatest attraction and/or repulsion. x'(t)=A, for t20 with x(0) = A = a. x(t)= b. C. 3 -11 d. x(t)= 2/2 [ ³3 ] 0 O a O b 32 x(t)= OC Od e. x(t)= Oc MNMN x(t)= - 2 3 = ²³2 [1] e -10t 32 3 1 3 2³/[³] e 3- e-101 + + NIN FIN ²2 [1] ²-8² +1/2 [13] -81 -101 + -101 e-8, (0,0) is an attractor -101 + -81, (0,0) is a repller -8t +²2[1]₁-8², (0,0) is an repller (0,0) is a saddle point. (0,0) is an attractor
Solve the initial value problem with [3] Classify the nature of the origin as an attractor, repeller, or saddle point of the dynamical system described Ax-b. Find the directions of greatest attraction and/or repulsion. x'(t)=A, for t20 with x(0) = A = a. x(t)= b. C. 3 -11 d. x(t)= 2/2 [ ³3 ] 0 O a O b 32 x(t)= OC Od e. x(t)= Oc MNMN x(t)= - 2 3 = ²³2 [1] e -10t 32 3 1 3 2³/[³] e 3- e-101 + + NIN FIN ²2 [1] ²-8² +1/2 [13] -81 -101 + -101 e-8, (0,0) is an attractor -101 + -81, (0,0) is a repller -8t +²2[1]₁-8², (0,0) is an repller (0,0) is a saddle point. (0,0) is an attractor
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![Solve the initial value problem with
2
5
Classify the nature of the origin as an attractor, repeller, or
saddle point of the dynamical system described Ax=b. Find the directions of greatest attraction
and/or repulsion.
x'(t)=A, for t≥0 with x(0) =
A=
-7 -1
3 -11
a. _x(t)=
C.
b. x(t)=
x(t)=
23/[3]e
1²11²31
= ³² [1] ₁²
31/ [3] e
e
23
3 3
³ [³₁]e-10¹ + [1]e-8¹ (0,0) is an attractor
е
d. x(t)=
e. x(t)=
O a
Ob
O C
Od
Oe
-10t+
+
-101 +
[]
2/1/1/3²1/0
e
101 +
1 le
-101
-8r
-81
-81
(0,0) is an attractor
(0,0) is a repller
(0,0) is an repliler
1 e-81, (0,0) is a saddle point.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd5246d2a-5796-4784-a543-e596d3b5542c%2F7fb7ada0-fbb2-4f92-adff-caa216323869%2F5j6msjp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Solve the initial value problem with
2
5
Classify the nature of the origin as an attractor, repeller, or
saddle point of the dynamical system described Ax=b. Find the directions of greatest attraction
and/or repulsion.
x'(t)=A, for t≥0 with x(0) =
A=
-7 -1
3 -11
a. _x(t)=
C.
b. x(t)=
x(t)=
23/[3]e
1²11²31
= ³² [1] ₁²
31/ [3] e
e
23
3 3
³ [³₁]e-10¹ + [1]e-8¹ (0,0) is an attractor
е
d. x(t)=
e. x(t)=
O a
Ob
O C
Od
Oe
-10t+
+
-101 +
[]
2/1/1/3²1/0
e
101 +
1 le
-101
-8r
-81
-81
(0,0) is an attractor
(0,0) is a repller
(0,0) is an repliler
1 e-81, (0,0) is a saddle point.
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