1. The problem statement, all variables and given/known data Solve the following systems by either substitution or elimination: dx/dt = y dy/dt = -x + cos(2t) 2. Relevant equations I know the solution is: x(t) = c_1cos(t) + c_2sin(t) - 1/3cos(2t) y(t) = -c_1sin(t) + c_2cos(t) + 2/3sin(2t) 3. The attempt at a solution x' = [ 0 1; -1 0][x; y] + cos(2t)[0; 1] Det(A-λI) = [-λ 1; -1 -λ] = λ^2+1 = λ_1 = i, λ_2 = -i λ = i; A-λi = [-i 1; -1 -i] (i)x + y = 0 x = 1, y = -i; v = [1; -i] = [1; 0] + i[0; -1] x(t) = c_1*cos(t) + c_2*sin(t); y(t) = c_1*sin(t) - c_2*cos(t); [0 1; -1 0]*a = [0; -1] a = [1; 0] [0 1; -1 0]*b = [1; 0] b = [0; 1] x(t) = c_1*cos(t) + c_2*sin(t) + cos(2t); y(t) = c_1*sin(t) - c_2*cos(t) + 1; I used the Undetermined Coefficients method: http://tutorial.math.lamar.edu/Classes/DE/RealEigenvalues.aspx#Ex1_Start I don't understand what I'm doing wrong and I've tried using variation of parameters but I end up with a bunch of trig that I can't make anything out of. If someone can point out my error and help with deriving the problem correctly I would really appreciate it.