Value of the Function
The solution of a differential equation is a function.  The value of the function is the output or result of a specific function.

Conserved Properties
A conserved property is a principle or aspect of a system which does not change with respect to time or any other variable.  Conserved properties are constant no matter what happens around them.

Initial Value Problem
Many mathematical models address how a system will evolve with time.  An initial value problem is a system of equations or relationships that will yield a specific predictive function when given a set starting value.

Additional Constraints
When modeling, it is sometimes insufficient to apply the obvious boundary conditions.  In order to yield a particular solution, some environments necessitate the application of additional constraints to fully define the system.

Normal Modes
Many systems have what are called natural or resonant frequencies, a speed of oscillation in which all components move together as a unit.  When a system has fallen into this pattern of motion, it is said to be in its normal mode.  Normal modes are very stabile, and depend on the structure, materials and boundary conditions of the system.

In the Domain of the Solution
The solution domain is the array of functions that satisfy the original differential equations or relationships.  Anything within the domain of the solution is a potential answer to the established problem.