University of Florida/Egm6321/F10.TEAM1.WILKS/Mtg5

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

Mtg 5: Thur, 03 Sept 09


Page 5-1

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Note: Eq.(2)p.4-2 and Eq.(4)p.4-2



Integrate from a to x:



, where ,


another way:

Where and






Page 5-2

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But

(1)



Eq.(3)p.4-2 : Why this form of nonlinear 1st order ODE?

Most general form:

(2)


Application:

(3)



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).

Page 5-3

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Form for exact nonlinear 1st order ODE:

is exact if a function such that

(1)



where:

is defined as "there exists"



Multiply Eq1) thru by to get:


Eq.(3)p.4-2  :


NOTE: If does not have the form:

(2)


Then cannot be exact.


Application: Eq.(3)p.5-2 is not exact because of the nonlinear term

Page 5-4

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Exactness test (continued)


p5-3 Eq(1):





Since


and


and


and


and

(1)


Application: Eq.(1)p.4-3 Not Exact







References[edit]