Question: inhomogenous differential equation system (Matrix)

Hey guys, I'm new to the forum, so please tell if I need to set up the question in a different way :) I've tried to find an answer for this, but have struggled since our learning book is in danish, so the used terms may not be technically correct,

 

Anyways, how do you solve this problem in maple? 

 

Find the complete real solution for the differential equation system:

 

 

For the homogenous part I've found. (Is this correct?)

  , c1,c2 € R

 

 

I've tried to find an answer for the inhomogenous part but I get a really complicated result, so I doubt it's correct.

 

Thanks for the help :)

-Alex 

 

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