We have the differential equation,
. The question asks to find the particular solution to the DE.
To find the particular solution look at the right-hand-side and make a “guess” of what the solution could be.
Since we have
we can guess that the particular solution could be in the form
, where
is some unknown constant.
Now finding the value of the unknown constant,
. Lets say
, find
and
.

=>

=>

Now plug
,
, and
into the given differential equation.
=>

=>

=>

=>

=>

Compare the coefficients,
=>

=>

So we can say our "guess" to the particular solution of the given differential equation is,
.