University of Florida/Egm6321/F10.TEAM1.WILKS/Mtg5

EGM6321 - Principles of Engineering Analysis 1, Fall 2009Edit

Mtg 5: Thur, 03 Sept 09


Page 5-1

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Note: Eq.(2)p.4-2 and Eq.(4)p.4-2

 

Integrate from a to x:

 

 , where  ,

 
another way:  

Where   and  

 

 

 

Page 5-2

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But  

 

(1)



Eq.(3)p.4-2 : Why this form of nonlinear 1st order ODE?

Most general form:

 

(2)


Application:

 

(3)



Where   is defined as  

HW: Show that   in Eq(3) is a nonlinear 1st order ODE.

Hint: Define the differential operator   associated with Eq(3).

Page 5-3

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Form for exact nonlinear 1st order ODE:

  is exact if   a function   such that

 

(1)



where:

  is defined as "there exists"

 

 

Multiply Eq1) thru by   to get:


Eq.(3)p.4-2  :  


NOTE: If   does not have the form:

 

(2)


Then   cannot be exact.


Application: Eq.(3)p.5-2 is not exact because of the nonlinear term  

Page 5-4

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Exactness test (continued)


p5-3 Eq(1):

 


 


Since  


and  


and  


and  


and  

 

(1)


Application: Eq.(1)p.4-3 Not Exact


 


 


 

ReferencesEdit