1. The problem statement, all variables and given/known data Find the general solution 2. Relevant equations x(t+2)-3x(t+1)+2x(t)=3*5^t+sin(0.5πt) 3. The attempt at a solution I start out by solving the homogeneous equation and end up with the two roots 1 and 2. Then I try to use the method of undetermined coefficients to find a particular solution. I guess that the solution is of the following form (I should probably include a cos term as well) u(t)=C*3*5^t+D*sin(0.5πt) then u(t+1)=C*3*5^(t+1)+D*sin(0.5π(t+1)) and u(t+2)=C*3*5^(t+2)+D*sin(0.5π(t+2)) I then insert these equations into the original equation to get C*3*5^(t+2)+D*sin(0.5π(t+2))-3*(C*3*5^(t+1)+D*sin(0.5π(t+1)))+2*(C*3*5^t+D*sin(0.5πt))=3*5^t+sin(0.5πt) move the terms around a bit to get 3*5^t(C*5^2-3*C*5+2*C)+D*sin(0.5π(t+2)-3*D*sin(0.5π(t+1))+2*D*sin(0.5πt)=3*5^5+sin(0.5πt) From the first part I see that (C*5^2-3*C*5+2*C)=1 so C=1/12 I would like to do something similar for the sin part of the expression, but I'm not sure how to handle it. I tried with sin(0.5π(t+2))=sin(0.5πt+π)=-sin(0.5πt) but then I don't know what to do with sin(0.5(t+1)). If anyone has any hints, tips or tricks I would be happy. I hope the equations are understandable otherwise I'll post them as a picture. Thanks in advance.