Solving for Particular Integral in Differential Equations: Arctan Definition

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Homework Help Overview

The discussion revolves around finding a particular integral for a differential equation, specifically focusing on the definition of arctan and its implications on the solutions derived. The original poster expresses confusion over obtaining two different answers based on the method used.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to reconcile two different solutions that arise from their methods, questioning whether the discrepancy is due to a misunderstanding of the arctan definition. Other participants note the similarity in the answers and point out a difference involving a sign, which leads to further clarification about the variables involved.

Discussion Status

Participants are actively engaging with the original poster's confusion, with some offering observations about the answers and others questioning the assumptions made regarding the variables. There is no clear consensus yet, but the dialogue suggests a productive exploration of the problem.

Contextual Notes

The original poster mentions an attachment that presumably contains the differential equation in question, which may be critical for understanding the context but is not visible in the discussion. Additionally, there is a reference to specific variables (a, b, c, w) that may affect the solutions, indicating potential constraints in the problem setup.

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Homework Statement


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.

The Attempt at a Solution


Attatched.

Thanks
 

Attachments

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?? You give just the answers and they look identical to me!
 
One has a plus thi one has a minus thi for some reason.
 
I think you mean phi, [tex]\phi[/tex]
I haven't read the question, I probably wouldn't understand it, but perhaps Halls was giving a hint that its equal to zero?
 
My mistake sorry, meant phi. I think phi's only going to be zero in a special case, for most values of a,b,c,w it's going to be non-zero.

Does anyone have any other suggestions? The second version is the one that works in the differential equation but I still can't see why the first one doesn't.
Thanks
 
Last edited:

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