anonymous
  • anonymous
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?
MIT 18.03SC Differential Equations
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
Where is this question in the MIT courseware? Or can you completely re-produce the question?
anonymous
  • anonymous
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?
anonymous
  • anonymous
here is the graph of the solution to the diffenrential equation |dw:1356597736417:dw| The question is here:http://ocw.mit.edu/courses/mathematics/18-03sc-differential-equations-fall-2011/unit-iv-first-order-systems/qualitative-behavior-phase-portraits/MIT18_03SCF11_s34_6text.pdf

Looking for something else?

Not the answer you are looking for? Search for more explanations.