Differential equation solving capabilities (for exact and numeric solutions) have been greatly enhanced by new algorithms and an interactive interface for solving ODEs. To learn about the DE updates, including the dsolve and pdsolve commands, see updates/Maple9/differential_equations.

The family of Mathieu functions has been added to Maple.  These are the solutions of Mathieu's equation

and their related support functions. The following are included.

2*Pi-periodic solutions ($\mathrm{MathieuCE}$, $\mathrm{MathieuSE}$)

General even and odd solutions ($\mathrm{MathieuC}$, $\mathrm{MathieuS}$)

Floquet solution ($\mathrm{MathieuFloquet}$)

First derivatives of the Mathieu functions. Higher derivatives can be represented in terms of the functions and their first derivatives using the differential equation.

Maple also implements the characteristic value functions ($\mathrm{MathieuA}$, $\mathrm{MathieuB}$) and the characteristic exponent function ($\mathrm{MathieuExponent}$).

For details, see Mathieu.

The new identify function is closely related to and dependent on the IntegerRelations package. It tries to determine the symbolic value of a floating-point number.

The SNAP package contains a new function QRGCD, which computes an approximate right GCD of two univariate polynomials. For more information, see SNAP[QRGCD].