One possible problem with your solution is that it contains
in the argument of cosine, when it should be a linear term. Aside from that, the best way to track down a mistake is to start from the beginning:
The mass's position function
satisfies the second-order ODE
(assuming there are no other external forces acting on the mass). The characteristic equation for this ODE is
which means the general solution to this ODE is
The angle difference identity for cosine allows you to condense the trigonometric part of the solution to
where
and
, leaving you with
These unknown constants can be found explicitly, as
and
.
Given that
and
, and the solution's first derivative is
you have the following system of equations needed to find
, and from there the corresponding values of
and
.
So the particular solution is
In terms of what you should submit, you would use
or rely on the exact forms in case rounded answers are not accepted.