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α2 Order of an ODE. Consider a function y = y (t). Let y (k) denote the k th derivative. For example,
dy
d2 y
,
y (2) = 2 ,
dt
dt
An ordinary diﬀerential equation is an expression in the form
F t, y, y (1) , y (2) , . . . , y (n) = 0
y (0) = y, y (1) = ··· for some function F . The largest order n of derivative y (n) which appears in this expression is called the
order of the diﬀerential equation. We give a few of examples.
Let x = x(t) denote the position of a mass m at time t under the inﬂuence of gravity and air resistance.
If this mass is near sea level (at the surface of the Earth), Newton’s Law of Gravity states dx
d2 x
+ m 2 = 0.
dt
dt
This is an ordinary diﬀerential equation of second order because it involves the second derivative of the
position x = x(t). If instead...
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This note was uploaded on 11/30/2011 for the course MATH 366 taught by Professor Edraygoins during the Spring '09 term at Purdue University.
 Spring '09
 EdrayGoins

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