We study rings of weak Jacobi forms invariant with respect to the action of the Weyl group for the root systems Cn and Dn, and provide an explicit construction of generators of such rings by using modular differential operators. The construction of generators in the form of a Dn-tower (n≥2) gives a simple proof that these graded rings of Jacobi forms are polynomial. We study in detail modular differential equations (MDEs), which are satisfied by generators of index 1. Interesting anomalies are noticed for the lattices D4, D8 and D12. In particular, some generators for these lattices satisfy the Kaneko–Zagier type MDEs of order 2 or MDEs of order 1 similar to the differential equation of the elliptic genus of three-dimensional Calabi–Yau manifolds. © 2024