1. The problem statement, all variables and given/known data This is an ordinary differential equation using the differential operator. Given the system: d^2x/dt - x + d^2y/dt^2 + y = 0 and dx/dt + 2x + dy/dt + 2y = 0 find x and y equation Answer: x = 5ce^(-2t) y = -3ce^(-2t) 2. Relevant equations 3. The attempt at a solution We change it into a differential operator equation... [D^2-1]x+[D^2+1]y = 0 [D+2]x +[D+2]y = 0 We simply cancel values out until we are left with 3x+5y = 0 [D+2]x +[D+2]y = 0 Here we have x = -5y/3 and y = -3x/5 We substitute into the second equation and we can easily find that x = ce^(-2t) y = ce^(-2t) My question is: How does the answer book know that there is a 5 for the x equation and a -3 for the y equation. It seems to me that the constant "c" handles this for me. Am I doing something wrong to get a less precise answer? Or did I work out this problem correctly. Thank you.