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

I'm trying to find a particular integral to the differential equation on the attatched image, but I come up with two slightly different answers depending on the method I use. I suspect the problem (if it's not just me being very thick and making a silly algebra error) is the way arctan is defined but I can't see what I should do differently in either solution.

3. The attempt at a solution

Attatched.

Thanks

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# Particular integral problem

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