Dynamical Systems

Question 1

what is the trajectory or solution curve and what point do you expect it to go through

Answer 1

{(t, g(t)); t ∈ IR} should pass through (t0, x0) which is determined by the initial condition x(t0) = x0

Question 2

flow

Answer 2

set of solution curves as the initial conidition varies

Question 3

form of explicit ODE
what is its general solution

Answer 3

dx/dt = f(t)
x(t) = F(t) + C

Question 4

what is required for a homogenous function to have a degree d

Answer 4

F(λx1, λx2, . . . λxn) = λ^dF(x1, x2, . . . xn) .

Question 4

form of a separable ODE

Answer 4

dx/dt = f(t) g(x).