Undergrad Is this PDF file the correct derivation?

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oliverkahn
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TL;DR
Given: Potential ##\psi(r)=constant##
To prove: ##u(r)=k_1+\dfrac{k_2}{r}##
My work is in the following pdf file:
 

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    V.pdf
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There is a lot of context missing.
 
Oh! I see. I was too hasty...Let me add some extra material in the beginning.
 

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