Suppose that one has 3 (complicated) functions $f(x)$, $g(x)$, and $h(x)$. I would like to use Maple to find any relations that may exist between these functions. For instance, if it so happens that $f(x)=5g(x)$, I would like to uncover that. Is there a Maple command which takes a set of `things' and compares them, with the goal of uncovering any relations that may exist.
It depends on what kind of relations you are expecting. If you think there is a linear dependence (with constant coefficients), take the vectors $\langle f(x), g(x), h(x) \rangle$ for (more than three) different values of $x$ and see if they are linearly dependent.
If you think there is a polynomial $P(f(x),g(x),h(x))=0$ of degree at most $n$, do the same for products...