User:Egm6322.s12.team2.steele.m2/Mtg11

=EGM6321 - Principles of Engineering Analysis 1, Fall 2011=

[[media:Pea1.f11.mtg11.djvu|Page 11-1]]
Euler Integrating factor method (IFM) p.10-6 cont’d [[media:Pea1.f11.mtg10.djvu|Eqn(1) p.10-6]]can be written as

Apply 2nd exactness condition [[media:Pea1.f11.mtg9.djvu|Eqn(3) p.9-3]] to find h:

Thus for (1) to be exact: Solving (4) for the integrating factor h(x,y) is usually not easy. R2.11: Explain why.

[[media:Pea1.f11.mtg11.djvu|Page 11-2]]
Consider 2 cases: Case 1: Suppose $$h_y(x,y) = 0$$, thus h is a function of x only; then (4) p.11-1 becomes: See (3) p.7-4

[[media:Pea1.f11.mtg11.djvu|Page 11-3]]
Case 2: Suppose $$h_x(x,y) = 0$$, thus h is a function of y only; then (4) p. 11-1 becomes: R*2.12: Find h using (1). Application: General non-homogeneous L1-ODE-VC If $$P(x) \neq 0 \ {\rm then} \ \forall x$$

[[media:Pea1.f11.mtg11.djvu|Page 11-4]]
Check condition (2) p.11-2:

[[media:Pea1.f11.mtg11.djvu|Page 11-5]]
=Application: Specific Non-Homogeneous L1-ODE-VC= It can be shown that R*2.13: Show (3). R*2.14: Solve the general L1-ODE-VC: To be continued…