1. The problem statement, all variables and given/known data The solution to the Initial value problem, x''+2x'+5x=0, is the sum of the steady periodic solution x_sp and x_tr. Find both. 2. Relevant equations 3. The attempt at a solution I already found x_sp ( the particular solution). It is (-44/533)cos(7t)+(14/533)sin(7t). r^2+2r+5=0 -1=+- 2i x_tr = e^(-t)(Acos(2t)+Bcos(2t)) x(t) = e^(-t)(Acos(2t)+Bsin(2t)) + (-44/533)cos(7t)+(14/533)sin(7t). x'(t) = e^(-t)(-2Asin(2t)+2Bcos(2t)) - e^(-t)(Acos(2t)+Bsin(2t)) + (308/533)sin(7t)+(98/533)cos(7t). x(0)=1(A+0)-(44/553) ==> A = 44/533 x'(0)= 1(2B)-1(A)+(98/533) ==> B= -27/533 So, x_tr=(44/533)cos(2t)-(27/533)sin(2t) this is not right however. Can someone see where I might have messed up?