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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
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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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.
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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