Register to reply 
Tow questions ( differential equation ) 
Share this thread: 
#1
May508, 12:16 PM

P: 6

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 


#2
May508, 01:54 PM

P: 6

please help me and i well be thanking for you



#3
May508, 01:58 PM

Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,682

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!



Register to reply 
Related Discussions  
Differential equation reducible to Bessel's Equation  Differential Equations  9  
Solving a partial differential equation (Helmholtz equation)  Differential Equations  7  
Differential equation questions, rate of change  Calculus & Beyond Homework  5  
Schrödinger equation: eigen value or differential equation  Quantum Physics  5  
Laplace's Equation and Seperation of Multivariable Differential Equation  Introductory Physics Homework  2 