This paper is devoted to considering the iterated order and the fixed points of some differential polynomials generated by solutions of the differential equation $$f^{{}^{\text{'}\text{'}}}+A_1\left(z\right)f^{{}^{\text{'}}}+A_0\left(z\right)f=F,$$ where $A_1\left(z\right)$, $A_0\left(z\right)$$(\neg \equiv 0)...$

Suppose that $f\left(z\right)$ is a meromorphic or entire function satisfying $P\left(z,f,f^{\prime },\mathrm{\dots },f^{\left(n\right)}\right)=0$ where $P$ is a polynomial in all its arguments. Is there a limitation on the growth of $f$, as measured by its characteristic $T\left(r,f\right)$? In general the answer to this question is not known. Theorems of Gol'dberg, Steinmetz and the author give a positive answer in certain cases. Some illustrative examples are also given.