I assume you mean you know how to find the homogeneous Solution?
Other wise The general solution is the sum of the homogeneous and particular solution.
If you have the general solution separate out the homogeneous solution and what's left is the particular solution.
Another way is if you use variation of parameters or reduction of order
omit the integration constants and you will obtain just the pariticular solution.
If you use undetermined coefficients you have just the particular solution.
in your problem the characeristic eqn is L^2 + 4L + 20 = 0
the solution is L = -2 + 4 i
the homogeneous solution consists of
y1 = e^(-2x)cos(4x) and y2 =e^(-2x)sin(4x)
Now you can use variation of parameters to find the general solution.