1. The problem statement, all variables and given/known data Find the general solution to d2y/dx2 +4y=cos(2x) 2. Relevant equations 3. The attempt at a solution I have woked out what I think is the Complementary function C1sin(2x)+C2cos(2x) the reason it is cos and sin is because the roots are 2i and therefore the exponential and imaginary number turn it in to a cos or sin. Particular Integral: y = a cos(2x) + b sin(2x) y' = -2a sin(2x) + 2b cos(2x) y'' = 4a cos(2x) - 4b sin(2x) ∴ -4a cos(2x) + 4b sin(2x) + 4a cos(2x) - 4b sin(2x) = cos(2x) but it all cancels out to give 0=cos(2x) which surely can't be right. Have I been staring at this so long that I cannot see the obvious answer?