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**There is a vector ##v_i(t)## (i=1,2,3). How to define the three functions in Mathematica?**What about ##t_{ij}(t,\vec{x})##?

I am trying to solve my vector and tensor equtions with Mathematica. Analytical solution would be perfect but numerical solution would also be fine. Actually I am not even sure whether Mathematica can deal with tensor equtions. Any help would be appreciated.