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

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

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

References[edit]