Differential Equations – Definitions and Terminology
An equation containing the derivatives of one or more dependent variables with respect to one or
more independent variables is said to be a
differential equation.
Examples:
Differential equations are classified by:
1) Type
a.
Ordinary Differential Equations
b.
Partial Differential Equations
2)
Order – The order of a differential equation is the order of the highest derivative in the
equation.
Note:
Don’t confuse the order of a derivative with the power to which the derivative is raised.
3) Linearity
An n
th
order ordinary differential equation is linear if and only if:
a)
The dependent variable and all its derivatives are to the 1
st
degree.
b)
Each coefficient depends at most on the independent variable
x
.
Examples of linear differential equations
Examples of nonlinear differential equations
Of course, what we will be concerned with in this course is finding solutions to differential equations.
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 Fall '10
 PamelaSatterfield
 Differential Equations, Equations, Derivative

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