1. Classify the stability type of the equilibrium point (0,0) of the following linear planar homogeneous...
3. Homogeneous linear systems with complex and repeated eigenvalues. Find the general solu- tion of the given system of differential equations. For the two-dimensional systems, classify the origin in terms of stability and sketch the phase plane (a) x'(t) y'(t) 6х — у, 5х + 2y. = (b) 4 -5 x'(i) х. -4 (c) 1 -1 2 x'() -1 1 0x -1 0 1
3. Homogeneous linear systems with complex and repeated eigenvalues. Find the general solu- tion of the...
Please find general solution and find the type and stability of critical point (0,0) x ]' = [1 2 [x [y -5 -1] y ]
(1 point) Classify the critical point (0,0) of the linear 2 x 2 system by computing the trace T, the determinant A and the discriminant D=72 – 4A. xt' = -5x + 3y, y' = 2x – 7y.
Classify or characterize the following systems as homogeneous,
additive, linearity, time-invariance, BIBO stability, causality,
invertible, and memoryless:
(a) y(n) = Re(a(n)), (c) y(n-2(4n + 1) (d) y(n)=x(-n) (e) y(n) = 2(n-2)-22(n-8) (f) y(n) = nx(n) (g) y(n) = Even{x(n-1))
Please do the problem step by
step. Thank you very much!
For the following linear systems with given eigenvalues, (a) Determine the type of equilibrium point at the origin; and (b) Describe the behavior of solution as t-> oo. 3. Eigenvalues are λ,--4, λ2-9. dr =5x + 4y dt dt
For the following linear systems with given eigenvalues, (a) Determine the type of equilibrium point at the origin; and (b) Describe the behavior of solution as t-> oo.
3. Eigenvalues...
Consider the system of differential equations Classify the critical point (0,0) as to type and determine whether it is stable, asymptotically stable, or unstable draw several (at least eight) trajectories in the xy-plane. 5 0 -5 5 0 -5
Classify each ode as linear or non linear, autonomous or not. If an ode is linear classify it as homogenous or non homogeneous. 1) y' = y 2) y = e-t sin y 3) y = y' +t > 4) = 1 5) (Int)y' = yey
Use the direction field to determine the stability of the point (0,2). [lmark] 1. .98- 1.96+- 0.02 0.04 0.06 0.08 0.1 A The point (0,2) is a stable equilibrium point. 8The point (0,2) is an unstable equilibrium point. Use the direction field to determine the stability of the point (0,0).I1mark] 2. 0.1 0.08 0.06 0.04 0.02- -- rt 0.02 0.04 0.06 0.08 0.1 A The point (0,0) is a stable equilibrium point. 8The point (0,0) is an unstable equilibrium point.
Find the general solution of the following system and determine the type and stability of critical point (0,0) [= [": 3] |
1
Sec. 8.1 8.2 Homework For each of the following systems, find all critical points (b) find the linearization at each critical point and determine the type and stability of each critical point (c) draw a phase portrait confirming the type and stability of all critical points (1) / - (2+)(y-*) V = (4-1)y + r) (2) 1-1- (4) 2 - 1 - ry (5) x = (1-1-y) V-(3--20) Bonus computational work (use technology!) 1. Uee pplane to plot the...