Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
zane120000
Group Title
i still can't understand that:
λ1 = 0 > λ2.
Line of critical points.
The critical points are not isolated –they lie on the line
through 0 with direction v1.
x = c1v1 + c2eλ2tv2
As t → ∞ x → c1v1 along a line parallel to v2.
why do the critical points lie on the line through 0 with direction v1?
 one year ago
 one year ago
zane120000 Group Title
i still can't understand that: λ1 = 0 > λ2. Line of critical points. The critical points are not isolated –they lie on the line through 0 with direction v1. x = c1v1 + c2eλ2tv2 As t → ∞ x → c1v1 along a line parallel to v2. why do the critical points lie on the line through 0 with direction v1?
 one year ago
 one year ago

This Question is Open

AddemF Group TitleBest ResponseYou've already chosen the best response.0
Where is this question in the MIT courseware? Or can you completely reproduce the question?
 one year ago

zane120000 Group TitleBest ResponseYou've already chosen the best response.0
I'm sorry I didn't make it clear. Suppose a matrix A has real eigenvalues with two independent eigenvectors. Let λ1, λ2 be the eigenvalues and v1 and v2 the corresponding eigenvectors. ⇒ general solution to the differential equation x'=Ax is x = c1e ^(λ1*t)v1 + c2e^(λ2*t)v2. when λ1 = 0 > λ2, The critical points are not isolated –they lie on the line through 0 with direction v1. x = c1v1 + c2e^(λ2*t)v2 As t → ∞ x → c1v1 along a line parallel to v2. why do the critical points lie on the line through 0 with direction v1?
 one year ago

zane120000 Group TitleBest ResponseYou've already chosen the best response.0
here is the graph of the solution to the diffenrential equation dw:1356597736417:dw The question is here:http://ocw.mit.edu/courses/mathematics/1803scdifferentialequationsfall2011/unitivfirstordersystems/qualitativebehaviorphaseportraits/MIT18_03SCF11_s34_6text.pdf
 one year ago
See more questions >>>
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.