User:EGM6341.s11.TEAM1.WILKS/Mtg19

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

[[media: 2010_09_30_15_51_32.djvu | Mtg 19:]] Thu, 30 Sep 10

[[media: 2010_09_30_15_51_32.djvu | Page 19-1]]
= Review =

= Non-exact L2-ODE-VC =

APPLICATION: [[media: Egm6321.f09/Lecture_plan | F09]]: Verify Exactness of Eq.(1). END APPLICATION

Recipe
For some special power forms (not $$ \sin x, \cos x ... \ $$) N1-ODE: $$ x^ay^b(py+qxy')+x^cy^d(ry+sxy') \ $$ Where $$ (a,b,c,d) \ $$ and $$ (p,q,r,s) \in \mathbb R \ $$ L2-ODE-VC: $$ \alpha\ x^ry''+ \beta\ x^sy'+ \gamma\ x^ty \ $$ Where $$ ( \alpha\, \beta\ , \gamma\ ) \ $$ and $$ (r,s,t) \in \mathbb R \ $$ Consider integrated factor $$ h(x,y)=x^my^n \ $$