(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Consider the equation [tex]\dot{x} = rx + x^3,[/tex] where [tex]r>0[/tex] is fixed. Show that [tex]x(t) \rightarrow \pm \infty[/tex] in finite time, starting from any initial condition [tex]x_{0} \neq 0.[/tex]

2. Relevant equations

I can think of none.

3. The attempt at a solution

The idea alone of x(t) approaching infinity in "finite time" throws me for a loop. Does this merely mean that |x(t)| becomes very large very quickly? That it is increasing (x > 0) or decreasing (x < 0) increasingly quickly as it "moves away from the origin"? It strikes me as impossible for something to "become infinite" in a finite amount of time. This is from Strogatz' "Nonlinear Dynamics and Chaos", Exercise 2.5.3 if you are interested.

Thank you!

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# Show that x(t) approaches infinity in finite time

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