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Question: Transform arbitrary ODE system into first order form

Imagine we have an ODE system 

odeSys := {diff(x(t),t$2)+diff(x(t),t)+x(t)=f(t),diff(y(t),t$2)+2*diff(y(t),t)+3*y(t)=g(t)};

It is easy to transform this system into a first order form by hand. But for larger systems, the procedure by hand becomes very error prone. Is there an intelligent way to transform a system of n scalar ODEs (order m) into a first order system? I know that the first order form is not unique. It is only important to reduce the system to a system of first order equations.

 

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