DIFFERENTIAL EQUATIONS DEFINITIONS
A Glossary of Terms
differential equation 
An equation relating an unknown
function and one or more of its derivatives
first order 
A first order differential equation contains no
derivatives other than the first derivative.
The order of a
differential equation should give the number of constants in
the general solution.
ordinary 
An ordinary differential equation has only one
independent variable
autonomous 
Describes a differential equation in which the
independent variable
t
does not appear explicitly, for
example,
dx
dt
x
x
=

4
2
initial condition 
A specified starting point such as
t
0
= 0
which represents a point on the graph from which the
solution curve begins
solution 
A solution for a differential equation is a function
whose elements and derivatives may be substituted into the
differential equation
general solution 
The general solution of a differential
equation contains an arbitrary constant
C
.
particular solution 
When an
initial value
is specified, a
solution (function) containing no constant
trivial solution 
All coefficients are equal to zero
isocline 
A line or curve formed by plotting constant values
of the first differential, i.e. points at which the slope is
uniform.
This is not necessarily a solution of
the
differential equation.
p20
separable 
A differential equation in which the dependent
and independent variables can be algebraically separated on
opposite sides of
the equation.
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 Spring '08
 comech
 Differential Equations, Equations, Derivative, Power Series, Periodicity, Partial differential equation

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