This article illustrates how ordinary differential equations and multivariate observations can be modelled and fitted with the brms package (Bürkner (2017)) in R1.
As an example I will use the well known Lotka-Volterra model (Lotka (1925), Volterra (1926)) that describes the predator-prey behaviour of lynxes and hares. Bob Carpenter published a detailed tutorial to implement and analyse this model in Stan and so did Richard McElreath in Statistical Rethinking 2nd Edition (McElreath (2020)).