first we solve the homogeneous difference equation:

we assume the solution is of the following form:

we now plug in this expression into the DE:

and solve for r:

r = 4, 2 thus:

now to find the particular solution we use the method of undetermined coefficients namely we assume that the solution has the form of the inhomogeneous term:

we proceed to substituting the particular solution in the DE:

so the general solution is:

now all you have to do is apply the initial conditions to find the constants...