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).

Deborah Wyatt 2022-07-23 Answered
Having trouble solving this separable differential equation
I am having some trouble with the following separable differential equation
d x d t = x ( x 1 ) ( x 3 )
with initial condition x ( 0 ) = 2. What is lim t x ( t ) ?
I am having some trouble with the logarithmic laws when solving for x ( t )
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Answers (1)

encoplemt5
Answered 2022-07-24 Author has 15 answers
You do not have to solve the differential equation
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.
Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more