Question

Due to DSolve syntax, systems of differential equations have to be given as lists of equations and not as a vector equation (Unlike Solve, which accepts both).
So my simple question is how to convert a vector equation such as:

{f'[t],g'[t]}=={{a,b},{c,d}}.{f[t],g[t]}

To list of equations:

{f'[t]==a*f[t]+b*g[t],g'[t]==c*f[t]+d*g[t]}

I think I knew once the answer, but I can’t find it now and I think it could benefit others as well.

Answer 1

Try using Thread:

Thread[{f'[t], g'[t]} == {{a, b}, {c, d}}.{f[t], g[t]}]
(* {f'[t] == a f[t] + b g[t], g'[t] == c f[t] + d g[t] *)

It takes the equality operator == and applies it to each item within a list with the same Head.