Question: how to apply dsolve to set of diff. equations in Matrix form?

Suppose one sets a system of differental equations in vector form, say 2 ODE's, like this:


Then to solve these, what would be an easy way to do it, without having to rewrite them again manually as a set, as what one would normally do. Clearly one needs to map dsolve, and also convert the vectors to a set somewhere? I am not able to get the syntax right.

Is there an easy way to automatically convert/rewrite the above to

ode2:= diff(x(t),t)=2*x(t)+y(t)  ,   diff(y(t),t)=3*y(t)-x(t);

so that I can just do


Or, a way to map dsolve directly into the first from as shown?( the Vector = Vector form).

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