(adsbygoogle = window.adsbygoogle || []).push({}); 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.

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# Homework Help: Solve this system of linear ODEs?

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