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Physics

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  • $\begingroup$ It doesn't appear that your solution is correct since, among other things it does not contain the $m^2$ factor in the article's differential equation. Fixing that should give you an equivalent solution for the field lines parametrically in s, which you can change to a function like theirs. Their function is not unique since any monotonic function of theirs gives another with the same contours. $\endgroup$
    – user200143
    Commented Jul 6 at 22:43