lec 11 - Tuesday, January 24 - Lecture 11 : Linear...

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Tuesday, January 24 Lecture 11 : Linear differential equations (Refers to Section 10.5 in your text) After having practiced the problems associated to the concepts of this lecture the student should be able to : Recognize a linear first order differential equation, solve a linear first order differential equation. We begin by reminding ourselves of the definition of a linear DE. Definition A Linear first-order differential equation is one which can be written in the form We can usually obtain an explicit solution from a linear differential equation rather than implicit solutions that are often obtained with separable DE’s. Examples of linear DE’s y ' + 2 y = e x xy ' + 2 y = 4 x 2 y ' + 2 xy = 2 x Note that the third DE is both separable and linear. 11.1 We solve a linear equation in two steps : 1. We first obtain the integrating factor where a can be fixed at any suitable value so as to get the simplest function for I ( x ). The integral in this expression simply means « an anti-derivative of the function
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This note was uploaded on 03/19/2012 for the course MATH 118 taught by Professor Zhou during the Winter '08 term at Waterloo.

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lec 11 - Tuesday, January 24 - Lecture 11 : Linear...

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