University of Florida/Egm6321/F10.TEAM1.WILKS/Mtg21

EGM6321 - Principles of Engineering Analysis 1, Fall 2009Edit

Mtg 21: Thurs, 8Oct09


Page 21-1

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P.20-4 (continued)

  is a homgenous solution  

 

2)   is another homogeneous solution since  

 

(Verify   and   are linearly independant components of  

3)   left hand side of Eq(1) p20-4   , where   is the 1st term on the right hand side

for  

4)   left hand side of Eq(1) p20-4   , where   is the 2nd term on the right hand side

for  

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Llinearity of ordinary differential equation   superposition

 

  , where  

Alternative method to obtain full solution for non-homogeneous L2_ODE_VC knowing only one homogeneous solution (e.g. obtained by trial solution) (bypassing reduction of order method2-undertermined factor for   and variation of parameter method)

Eq.(1) P.3-1 =  

Assume having found  , a homogeneous solution:  

Consider:   , where   is an undetermined factor



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Follow the same argument as on P.17-2 to obtain:

 

(1)

NOTE: this equation is missing the dependant variable   in front of   term due to reduction of order method  

 

(2)



 

(3)

where   and   are known

Non-homogeneous L1_ODE_VC solution for   : Eq.(4) P.8-2

 

(4)



 

(5)



ref: K p.28, problem 1.1ab

a)   ,  

Trial solution   , where   constant

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Find  

How many valid homogeneous solutions to  , find   using undetermined factor method


ReferencesEdit