  In this paper we obtain an ordinary differential equation ${\sf H}$ from a
Picard-Fuchs equation associated with a nowhere vanishing holomorphic $n$-form.
We work on a moduli space ${\sf T }$ constructed from a Calabi-Yau $n$-fold $W$
together with a basis of the middle complex de Rham cohomology of $W$. We
verify the existence of a unique vector field ${\sf H}$ on ${\sf T }$ such that
its composition with the Gauss-Manin connection satisfies certain properties.
The ordinary differential equation given by ${\sf H}$ is a generalization of
differential equations introduced by Darboux, Halphen and Ramanujan.
