EGM6321 - Principles of Engineering Analysis 1, Fall 2009
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Mtg 17: Thur, 10Oct09
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
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(1)
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Where can be substituted for
or in Eq(1)
Given one homogeneous solution known
Find second homogeneous solution such that
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(3)
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Where are constants
Assume full homogeneous solution
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(2)
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Where is an unknown to be determined
Where is known
"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
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(1)
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Solve for Z,
- integration factorial method (HW)
- Direct integration (because Eq(1) is homogeneous)
Where are known
Integrate , where k is a constant
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(2)
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where
where
Homogeneous solution
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(1)
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where and
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(2)
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HW: obtain Eq.(2) P.17-3 using the integrating factor method