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1.1 Some Elements of the Theory

A differential equation is an equation involving an unknown function and one or more of its derivatives. The equation is an ordinary differential equation (ODE) if the unknown function depends on only one independent variable. Some examples of ODEs follow:

In (1--5) t is the independent variable; the dependent variables are , and p, respectively.

In what follows we will frequently use the notation to represent , to represent , to represent , and, in general, to represent .