lecture_3 (dragged) 2

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

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

## 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.

Ask a homework question - tutors are online