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

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EGM6321 - Principles of Engineering Analysis 1, Fall 2009[edit]

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

Page 21-2

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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



Page 21-3

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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

Page 21-4

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Find

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


References[edit]