No, that's not true in general. Try v=1, and that is clear. It does make an interesting equation though. Can you solve it?Hi,
I'm almost certain this is a silly question, but is the following correct :
dv/dt = 1 / (∫1/v dt)
(the differential of v is the same as the reciprocal of the integral of the reciprocal of v ...if that helps )
Thanks very much!
That's an interesting thought. I'll have to think about that a little to see if it holds up rigorously. I can see how you are thinking that.Thanks for the reply.
Is it that dV = V, so it is correct only when V is infinitely small ?
I think that would make sense!
Hmmm, I got something different. We should both double check.I find that An = -An, so surely this would only work when A or n are zero? So v is independent of t ?
You are getting closer. Try v=At^(1/2). Basically, A can be anything but n needs to be 1/2.My algebraic integration clearly isn't as good as it should be! ^
An = -A(n+1)
so this would suggest that the constraint is that n = -1/2.
Although I've tried to do it again with v = At^(-1/2) but it didn't add up unless A was 0
There is even a more general solution. It should be clear now that any scale factor in front will cancel out automatically. What about A(t-B)^n? The above shows that n=1/2 and B=0 works. Are there other possible solutions?Ahh, great, thanks.
It all adds up now!
Thanks very much for your help !
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