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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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... $\displaystyle \displaystyle \begin{align*} \int{\frac{dx}{x^2 + 2x - 3}} = \int{1\,dt} \end{align*}$
Are you saying that you do not know how to integrate that? The denominator can be factored and then you can use "partial fractions".
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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