This polynomial is linear in the variable t. It is
followed by the
statement "Its Riccati differential equation is
separable one" and the
fairly simple differential equation:

dif(x(t),t) = -(x(t)^2 + m x(t) + r) / (t^2 + (-2 h -
m) t - 2 k + 13
r)

The equation contains two variables m,k in addition
to those found in
the polynomial. Its integration leads to a functional
relation between
x and t that involves logarithms and square roots.

As such, the multivariate polynomial and the
differential equation are
unobjectionable; the problem now is that your
accompanying words have
no recognizable mathematical meaning:

In what sense are your "polynomials based on
Ricatti"? (Is "Ricatti"
here short for "some Ricatti differential equation"
or for "Jacopo
Francesco Riccati"?) How does your differential
equation with a
logarithmic solution "generate" your polynomial?

More genearally speaking, your comments seem to imply
some relation
between the high-order polynomial and the fairly
simple differential
equation. If that is what you mean, what use do you
think can this
relation be put to?

Martin.