# Thread: Critical points and stability problems

1. ## Critical points and stability problems

Nonlinear ODE, dx/dt=2x+x^2-3

A. Solution with following initial conditions,
(t,x)=(-2, 3)
(t,x)=(-2, 1)
(t,x)=(-2, 0)
(t,x)=(-2, -3)
(t,x)=(-2, -5)

B. Finding critical points and commenting stability

2. ## Re: Critical points and stability problems

Originally Posted by tykim
Nonlinear ODE, dx/dt=2x+x^2-3

A. Solution with following initial conditions,
(t,x)=(-2, 3)
(t,x)=(-2, 1)
(t,x)=(-2, 0)
(t,x)=(-2, -3)
(t,x)=(-2, -5)

B. Finding critical points and commenting stability
It's separable...

\displaystyle \displaystyle \begin{align*} \int{\frac{dx}{x^2 + 2x - 3}} = \int{1\,dt} \end{align*}

3. ## Re: Critical points and stability problems

Are you saying that you do not know how to integrate that? The denominator can be factored and then you can use "partial fractions".

4. ## Re: Critical points and stability problems

The Critical point is when the dx\dt=0. Stability is factoring the quadratic. And use the differantial equation graph to know what is the stability.