lec 12 - Wednesday, January 25 - Lecture 12 : Second-order...

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Wednesday, January 25 Lecture 12 : Second-order Differential equations . (Not explicitly discussed in your text) After having practiced the problems associated to the concepts of this lecture the student should be able to : Solve second-order differential equations which can be reduced to a first order DE. Normally these are second order DE’s where there is a variable missing. 12.1 Second-order equations can always be expressed in the form F ( x , y , y ', y '') = 0. There are two types of second-order differential equations for which we have relatively easy methods of solution. We study them below. Remarks In the examples below you will note that initial value problems for second order differential equations have two initial conditions: y '( a ) = b and y ( c ) = d . Also note that in the following examples v = v ( x ) and y = y ( x ) and so all their derivatives are with respect to x . 12.1.1 Type I :
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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 12 - Wednesday, January 25 - Lecture 12 : Second-order...

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