Having trouble solving this separable differential equation I am having some trouble with the following separable differential equation (dx)/(dt) = x(x-1)(x-3) with initial condition x(0)=2. What is lim_(t -> oo) x(t) I am having some trouble with the logarithmic laws when solving for x(t).

Question

Having trouble solving this separable differential equation
I am having some trouble with the following separable differential equation

\frac{d x}{d t} = x (x - 1) (x - 3)

with initial condition

x (0) = 2

. What is

lim_{t \to \infty} x (t)

?
I am having some trouble with the logarithmic laws when solving for

x (t)

Answer 1

You do not have to solve the differential equation

\frac{d x}{d t} = x (x - 1) (x - 3)

to answer the question.
Note that you have three equilibrium points, namely

x = 0, 1, 3

Qualitative analysis of these equilibrium points show that

x = 1

is asymptotically stable.
Thus starting at

x (0) = 2

the solution will tend to

x = 1.

Answers (1)