Please can you solve this tow questions today.... Q1) If g is a function such that g(0)=0 and all high order derivatives exist consider the autonomous system dx/dt = g(y) dy/dt = g(x) a. show that (o.o) is critical point and that system is almost linear in the neighborhood of (o.o) b. show that if g'(o)>o then critical point (o,o) is unstable and that if g'(o)<o then the critical point is asymptotically stable c. show that the critical point (o,o) is a saddle point and unstable Q2) consider the system dx/dt =f(y) dy/dt =g(x) where f,g are functions whit all their higher derivatives exist and f(o)=g(o)=o and f'(0)≠0 g'(o)≠o a. show that (o.o) is critical point of the system and the system is almost linear system at it. b. show that if f'(0)g'(0)>0 then the critical point (0.0) is a saddle point and if f'(0)g'(0)<0 then the critical point (0.0) is a center or spiral point thank you شكراً كتير مقدماً
Please start by reading the files you were supposed to have read when you registered for this forum! You will not get any "help" if you refuse to even TRY doing the problem yourself!