Question

Without solving explicitly, classify the critical points of the given first-order autonomous differential equation as either asymptotically stable or unstable. All constants are assumed to be positive. (Enter the critical points for each stability category as a comma- separated list. If there are no critical points in a certain category, enter NONE.) dv m = tg - ky dt asymptotically stable VE unstable V mg k х Need Help? Read 1 Talk to a Tutor 2. (-/1 Points] DETAILS ZILLDIFFEQ9 10.3.008. MY NOTES Without solving explicitly, classify the critical points of the given first-order autonomous differential equation as either asymptotically stable or unstable. All constants are assumed to be positive. (Enter the critical points for each stability category as a comma separated list. If there are no critical points in a certain category, enter NONE.) dx dr =kla - x)(8 - x)(8 - x), a > > asymptotically stable unstable

Answer 1

dn X > B>2 dt re 2, B1 are = k18-9) (B-1)(3-1) the critical points (2-1) (B-9) (300 dan at + + + + 7 M = + + x=p + n = X - al and a=x) » =3 / assow diverging Unstable n=1 arrows converging → asymptotically stable :- Stable B Unstable x = a and 2 CS Scanned with CamScanner