EGM6321 - Principles of Engineering Analysis 1, Fall 2009
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Mtg 13: Tues, 22Sept09
Euler integrating factor method Eq.(1) P.12-3
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(1)
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Where:
HW: Find (m,n) such that Eq(1) is exact.
Result: A first integration is:
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(2)
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Where and and are constants
HW: Solve Eq(2) for HINT: L1_ODE_VC (integrating factor)
A class of exact L2_ODE_VC (how to invent more exact L2_ODE_VC)
HW: Find mathematical structure of that yields the above class
Where and
and and and
Answer:
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(1)
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Eq.(2) P.13-1 : and and
Exact Nn_ODE's, where N means nonlinear and n means nth order
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(2)
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Where and and
Condition 1 for exactness:
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(1)
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Where is related term by term to
Condition 2 of exactness: , where
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(2)
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HW: Case (N1_ODE)
HINT:
Case (N2_ODE)