Solving a 2 d.o.f. spring-mass-damper system

I've got all the matrices in state-space form, but how do I solve them? I tried integrating the equations one by one, but it seems like I end up with more variables than equations.

Thanks for any help, I'm completely lost.
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 Posting the equations of your problem would help. In case it helps, remember that you have 2 extra equations from w1=y1', w2=y2'

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