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## Homework Statement

Solve this system of linear ODEs:

**1) x''(t) = x + y**

2) y''(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!

## Homework Equations

See above.

## 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.