Modeling with Differential Equations

The most basic differential equation model is one that is composed of a single first order differential equation. This kind of model is used to represent the dynamics of a single state variable. The most basic type of first order differential equation model is constructed by identifying all of the various interactions or events that cause a change in the state variable of interest. Analytical solutions are exact, and can be algebraically manipulated to answer a variety of questions. Numerical solutions are approximate and subject to some level of error. Industrial Occupations University is a local trade school that wants to grow its enrollment. In deriving differential equation models of higher order, people need o consider a state variable of interest and formulate an equation based on the state variable and its derivatives which dictate the dynamics of the desired system.