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Can odesolve be used for systems of equations? Like:
y1''=-b1*y1'-k1*y1-k2*(y1-y2)=b2*y1'-y2')+1
y2''=-b2*(y2'-y1')-k2*y2-y1)

Yes, but the system must be rewritten as a system of order 1.
Note that your example is linear with constant coefficients and can be solved exactly by desolve, once rewritten as a system of order 1.

I understand. Thank you.