A community for students. Sign up today!
Here's the question you clicked on:
 0 viewing
 2 years ago
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?
 2 years ago
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?

This Question is Open

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

zane120000
 one year ago
Best ResponseYou've already chosen the best response.0I'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?

zane120000
 one year ago
Best ResponseYou've already chosen the best response.0here 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
Ask your own question
Ask a QuestionFind more explanations on OpenStudy
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.