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Let y k denote the k th derivative for example dy d2

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Unformatted text preview: tions. 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.

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