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Math Help - Critical points and stability problems

  1. #1
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    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
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  2. #2
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    Re: Critical points and stability problems

    Quote Originally Posted by tykim View Post
    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 \begin{align*} \int{\frac{dx}{x^2 + 2x - 3}} = \int{1\,dt} \end{align*}
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  3. #3
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    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".
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  4. #4
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    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.
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