1. The problem statement, all variables and given/known data Consider the second order differential equation y'' - 4y' + 4y = f(x) Find a particular solution if f(x) = 25cos(x) 2. Relevant equations I believe for this type of question I should let y = Asin(x) + B cos(x) Hence y' = Acos(x) - Bsin(x) and y'' = -Asin(x) - Bsin(x) 3. The attempt at a solution I think everything above is right, and for the rest of the question I should just be able to substitute back into the original formula and find values for A and B. The problem is when I do substitute back in all I get is a mess and a headache! Here is what I got by substitution: -Asin(x) - Bcos(x) - 4[Acos(x) - Bsin(x)] + 4[Asin(x) + Bcos(x)] = 25cos(x) Hence -Asin(x) + 4[Asin(x) + Bsin(x)] - Bcos(x) - 4[Acos(x) - Bcos(x)] = 25cos(x) That's about all I think I can do and I have no idea how to obtain values for A and B. I know the answer is y(p) = 3cos(x) - 4sin(x). How to get this answer from the above I have no idea, I'm obviously missing something. Thanks in advance for any advice or help.