(A) semi-stable and unstable (B) asymptotically stable and asymptotically stable
ID: 2875371 • Letter: #
Question
(A) semi-stable and unstable (B) asymptotically stable and asymptotically stable (C) asymptotically stable and unstable (D) asymptotically stable and semi-stable (E) unstable and asymptotically stable (F) unstable and semi-stable (G) semi-stable and semi-stable (H) semi-stable and asymptotically stable (I) unstable and unstable
Consider the following autonomous first order differential equation. dy/dx= ((y 4)^2)*(y + 9)The critical points are y = 4 and y = 9. Classify these critical points (in the given order) as asymptotically stable, unstable, or semi-stable.
(A) semi-stable and unstable (B) asymptotically stable and asymptotically stable (C) asymptotically stable and unstable (D) asymptotically stable and semi-stable (E) unstable and asymptotically stable (F) unstable and semi-stable (G) semi-stable and semi-stable (H) semi-stable and asymptotically stable (I) unstable and unstable
Explanation / Answer
We have given y = 4 and y = 9 and we can see that these two critical poitns are real and of opposite sign.
We know that if critical points are of opposite sign then the critical point is called saddle points and always unstable.
(I) is coorect option.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.