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I am interested in solving systems of ODEs symbolicly, keeping things with arbitrary dimensions for clarity. For example, assume that $x, f(x) \in R^N$ and $A \in R^{N \times N}$, how do I solve $f'(x) = A \cdot x$ ? (of course, I am interested in much fancier equations)

From the Mathematica documentation on symbolic tensors, it talks about differential operators but I can't figure out the notation. For example, I tried variations of the following, which didn't work:

$Assumptions = A \[Element] Matrices[{2, 2}, Reals] && x \[Element] Vectors[2, Reals] && f[x] \[Element] Vectors[2, Reals];
DSolve[ A . f[x] == D[f[x], x], f[x], x]

I also tried Grad, etc. but didn't work. Any ideas on whether this is possible?

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