User:Egm6321.f10.team4.Yoon/Mtg22

=EGM6321 - Principles of Engineering Analysis 1, Fall 2010=

[[media: 2010_10_08_17_07_22.djvu | Mtg 22:]] Fri, 8 Oct 10

= Non-exact L2-ODE-VC, integrating factor (cont'd) =

[[media: 2010_10_08_17_07_22.djvu | Page 22-1]]
where m,n $$\displaystyle \in \mathbb{R}$$to be determined.

Application
For application on [[media: 2010_09_30_15_51_32.djvu | Eq (1), p.19-1]]:

F09: solve L1-ODE-VC Eqn. (3) for y(x)(IFM)

= Mathematical Structure of first integral for a class of "exact" L2-ODE-VC =

First integral $$\displaystyle \phi$$

[[media: 2010_10_08_17_07_22.djvu | Page 22-2]]
Consider the L2-ODE-VC:

Answer:

See [[media: Egm6321.f09.mtg13.djvu |F09 p.13-1]] for the homework problem statement on derivation of Eqn.(3).

Application: Select $$\displaystyle \phi$$ satisfying Eqn.(3)

[[media: 2010_10_08_17_07_22.djvu | Page 22-3]]
= Exact Nn-ODE's (Non-linear nth order)=

Exactness Condition 1:

[[media: 2010_10_08_17_07_22.djvu | Page 22-4]]
Exactness Condition 2:

Case n=1: N1-ODE

[[media: 2010_10_08_17_07_22.djvu | Page 22-5]]
See [[media: egm6321.f09.mtg13.djvu | F09 Mtg 13]] for more details.