EGM6321 - Principles of Engineering Analysis 1, Fall 2009
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Mtg 5: Thur, 03 Sept 09
Note: Eq.(2)p.4-2 and Eq.(4)p.4-2
Integrate from a to x:
, where ,
another way:
Where and
But
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(1)
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Eq.(3)p.4-2 : Why this form of nonlinear 1st order ODE?
Most general form:
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(2)
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Application:
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(3)
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Where is defined as
HW: Show that in Eq(3) is a nonlinear 1st order ODE.
Hint: Define the differential operator associated with Eq(3).
Form for exact nonlinear 1st order ODE:
is exact if a function such that
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(1)
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where:
is defined as "there exists"
Multiply Eq1) thru by to get:
Eq.(3)p.4-2 :
NOTE: If does not have the form:
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(2)
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Then cannot be exact.
Application: Eq.(3)p.5-2 is not exact because of the nonlinear term
Exactness test (continued)
p5-3 Eq(1):
Since
and
and
and
and
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(1)
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Application: Eq.(1)p.4-3 Not Exact