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

Consider the ODE x' = x^{2}+ ε, where ε is a small number. Find the time T = T(ε) it takes for the solution to travel from x = -∞ to x = ∞.

Let T_{1}= T_{1}(ε) be the time it takes the particle to travel to x = -1 to x = 1. Show that T/T_{1}→ 1 as ε → 1.

2. Relevant equations

Uhmm... we haven't really learned any yet. This is qualitative analysis of ODEs.

3. The attempt at a solution

I have no idea where to start really. I thought that to find time, we could treat x' as a velocity, and find the position function by integrating x'. Once we had this position function, I thought it would be okay to divide position by velocity to find time... but I don't even know what that would represent! From negative infinity to infinity, no less...

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# Homework Help: Time to Travel to One Infinity and Back?

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