University of Florida/Egm6321/F10.TEAM1.WILKS/Mtg17

EGM6321 - Principles of Engineering Analysis 1, Fall 2009Edit

Mtg 17: Thur, 10Oct09


Page 17-1

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Linearity   superposition  

Homogeneous Solution  
- Euler Equations
- Trial solution (undefined coefficient)
- Reduction of order method 2: Undetermined factor

Homogeneous L2_ODE_VC: cf. Eq.(1) P.3-1

 

(1)



Where   can be substituted for   or   in Eq(1)

Given one homogeneous solution   known

Find second homogeneous solution   such that

 

(3)



Where  are constants

Assume full homogeneous solution

 

(2)



Where  is an unknown to be determined

Where  is known

Page 17-2

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"Full" = includes  

Add the following:  

and  

and  

To get   by Eq(1) p17-1

Reduce to  

Since   is a homogeneous solution  , NOTE missing dependent variable U in front of   term

Let   homogeneous L1_ODE_VC for Z

Page 17-3

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(1)



Solve for Z,
- integration factorial method (HW)
- Direct integration (because Eq(1) is homogeneous)

 

Where   are known

Integrate  , where k is a constant

 

(2)

where  

 

where  

Page 17-4

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Homogeneous solution

 

(1)



where   and  

 

(2)



HW: obtain Eq.(2) P.17-3   using the integrating factor method

ReferencesEdit