Given $y,f: \mathbb{R^{+}} \rightarrow \mathbb{R}^{n}$ consider the fist order ODE system:
$\overset{.}{y}=f(y(t),t)$
We know that thas System is conservative if the divergence of $f$ (given it's exists) is null.
We also know that the vector field of the tangent vectors given by $f$ is conservative iff exists a function such that it's gradient is $f$.
Is there any relation between these two definitions?