1. The problem statement, all variables and given/known data The higher order equation y"+y=0 can be written as a unknown d/dt[y y']=[y' y"]=[y' -y] If this is du/dt=Au, what is the 2x2 matrix A? Find its eigenvectors and eigenvalues, and compute the solution THAT STARTS FROM y(0)=2, y'(0)=0. 2. Relevant equations y'=Ay y(0)=y0 3. The attempt at a solution I found matrix A [0 1 -1 0]. The eigenvalues are i and -i, and the eigenvectors [1 -i]^T [1 i]^T I found the geneal solution to be: y(t) = c1eit[1 i]^T+c2e-it[1 -i]^T Which is equivalent, y(t)=c1[cos(t) -sin(t)]^T + c2[sin(t) cos(t)]^T I just don't know how to incorporate the initial conditions that y(0)=2 and y'(0)=0??? Any ideas???