It feels like a stupid question...

given the system:

with x=x(t), y=y(t)

How would I rewrite the system in, say ?

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- Sep 30th 2010, 04:47 AMDinkydoeRewriting a ODE in -t
It feels like a stupid question...

given the system:

with x=x(t), y=y(t)

How would I rewrite the system in, say ? - Sep 30th 2010, 05:18 AMAckbeet
Well, you have an autonomous system there, meaning that you don't have to worry about the RHS's so much. Try this:

- Sep 30th 2010, 08:10 AMDinkydoe
Doesn't this just give...

Don't we also want to have in our equations?

How do we deal with that? - Sep 30th 2010, 08:14 AMAckbeet
Can't you just make the substitution outright? I'm thinking

Wouldn't that do the job? - Sep 30th 2010, 08:19 AMDinkydoe
I don't see how we could just make that step...

Gives...

I don't see how we could just subtitute in the eqations... - Sep 30th 2010, 08:22 AMAckbeet
Do x and y represent physical quantities of any sort?

- Sep 30th 2010, 08:24 AMDinkydoe
No, they do not specifically represent anything...

So, if we want to rewrite a system in , i don't see why can simply be replaced by - Sep 30th 2010, 08:27 AMAckbeetQuote:

No, they do not specifically represent anything...

I don't have any other answer, I'm afraid, other than I think you can just do it. I don't have a justification. This is the physicist part of me talking, I freely admit.