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Order of Ordinary Differential Equations
An
ordinary
differential equation is an equation for one unknown function
x
(
t
)
of a single
independent variable
t
that involves one or more of
the unknown’s derivatives:
dx
dt
First Derivative
,
d
2
x
dt
2
Second Derivative
,
d
3
x
dt
3
Third Derivative
,
,
d
n
x
dt
n
n
th
Derivative
If the independent variable is time, the derivatives are often denoted by dots as shown below.
x
First Derivative
Velocity
,
x
Second Derivative
Acceleration
,
x
3rd Derivative
Jerk
,
x
4
th
Derivative
Snap
,
x
5
th
Derivative
Crackle
,
x
6
th
Derivative
Pop
If the unknown
x
(
t
)
represents the location or position of a point particle, these derivatives are called the velocity
, acceleration
, jerk
and snap
respectively. The fifth and sixth derivatives have been called the crackle
and pop
. Some authors have given the snap other appellations
including jounce
, sprite
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 Spring '08
 Hrebian
 Derivative, dt

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