1. The problem statement, all variables and given/known data Solve this system of linear ODEs: 1) x''(t) = x + y 2) y''(t) = x + y Just fyi, this is part of a much larger problem but I need to solve this system! 2. Relevant equations See above. 3. The attempt at a solution Okay so I think the most logical way to solve this would be to set x''(t) = y''(t). Then x''(t) = y''(t) x' = y' + c1 x = y + c1t + c2 which implies 3) x'' = 2x - c1t - c2 4) y'' = 2y + c1t + c2 But I am not sure what to do from here. Apparently there should be 4 arbitrary constants in the final answer. But wouldn't solving x'' for x give you 2 and then solving y'' for y give you two more? Thanks for any help.