Orange Coast College: Math A285: Differential Equations 1.1: Definitions and Terminology| Instructor: Scott Northrup

Math A285
Di↵erential Equations §1.1: Definitions and Terminology


Instructor: Scott Northrup




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, Definition: Di↵erential Equation
An equation containing derivatives of one or more unknown
functions (or dependent variables), with respect to one or more
independent variables, is said to be a di↵erential equation (DE).
We can classify them by type, order, and linearity
I Type. If the equation has derivatives with respect to a single
independent variable, the equation is said to be an ordinary
di↵erential equation (ODE). If the equation involves partial
derivatives of functions of two or more independent variables,
it is called a partial di↵erential equation (PDE).
I Order. The order of a di↵erential equation is the order of
the highest derivative in the equation.
I Linearity. The general form of an ordinary di↵erential
equation is F (x, y , y 0 , . . . , y (n) ) = 0. We say the ODE is
linear if it has the form

an (x)y (n) + an 1y
(n 1)
+ · · · + a1 (x)y 0 + a0 (x)y + g (x) = 0


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