Solving for Particular Integral in Differential Equations: Arctan Definition

[Zell2]

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

 

[HallsofIvy]

?? You give just the answers and they look identical to me!

 

[Zell2]

One has a plus thi one has a minus thi for some reason.

 

[Gib Z]

I think you mean phi, $$\phi$$
I haven't read the question, I probably wouldn't understand it, but perhaps Halls was giving a hint that its equal to zero?

 

[Zell2]

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