Please give the complete solution. Do not copy and paste. Thank you so much!

Problem 3: Solve the following recurrence equation: P1-1 +5P-2 +3P..-3 + 16 - 3 0 P, P P2 4 22 Show your work (all steps: the associated homogeneous equation, the characteristic polynomial and its roots, the general solution of the homogeneous equation, computing a particular solution, the general solution of the non-homogeneous equation, using the initial conditions to compute the final solution.)