User:EGM6341.s11.TEAM1.WILKS/Mtg19

EGM6321 - Principles of Engineering Analysis 1, Fall 2010

Mtg 19: Thu, 30 Sep 10

Non-exact L2-ODE-VC

APPLICATION:

$\displaystyle \begin{align} \sqrt{x} y''+2xy'+3y=0 \end{align}$

(1)

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 \$

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