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

I'm examining the equation Ohm_Max + dOhm/dr = Ohm_Max - dOhm/dr and can't find any solutions other than the trivial one, Ohm(r) = 0 for all r.

It's meant to determine if it is possible to build a length of conductor such that, upon dividing it at any arbitrary point, you'll find that the resistance behind is the same as the resistance ahead.

3. The attempt at a solution

Ohm(r) = 0. You can't have one because if Ohm(r) is even then dOhm/dr is odd.

Ohm(r) = Ohm_Max at r = 0 for bounds -L/2 to L/2, captured in the use of Ohm_Max the constant.

So the integral from -L/2 to 0 must equal the integral from 0 to L/2 meaning that dOhm/dr has to be even. This can't be as if Ohm(r) is odd then Ohm(0) must be 0 and not Ohm_Max. Odd functions cannot be valued at 0.

Now, mathematically why can't this work? I apologize for the absence of TeX. I'm still getting used to the forum interface.

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# Does this differential equation have a solution?

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