User:Egm6322.s12.team2.steele.m2/Mtg24

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

[[media:Pea1.f11.mtg24.djvu|Mtg24]] Tue, 11 Oct 11
'''Note: Images could not be found for these complicated flow patterns of using differential equations. So only text entry was done. (Manuel Steele - summer 2012). For images and decision flow, please see djvu file above in bold link.'''

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Mtg 24: Tue, 11 Oct 11

Plan: Summary of ODE solution methods Flow Chart Exact Nn-ODE’s (Non-linear nth order) Case n=2: N2-ODE 2nd exactness condition Method 1 p.22-4 cont’d Method 2

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=General ODE nth order 2nd order Nn-ODE LN-oDE-VC= 1st order N1-ODE N2-ODE p.24-3 L2-ODE-VC p.24-2 L1-ODE-VC Missing y(x) Exact or made exact by IFM  Non-exact 0th order eq. for p(x) 0th order eq. for y(x) Other methods analytical numerical P(x) y(x) $$y(x) = \int p(x)dx$$

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2nd order p.24-1 N2-ODE p.24-3 L2-ODE-VC Non-exact Missing y(x)                                  Power form Exact or made exact by IFM

L1-ODE-VC for p(x)                      L1-ODE-VC for y(x)           N1-ODE p.241

P(x)                                                     y(x)                      Other methods:  analytical, numerical

$$y(x) = \int p(x)dx$$                                             Special L2-ODE-VC:  Legendre, Bessel, Laguerre, Hermit, etc.

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N2-ODE p.24-1

Missing                                                          Exact                                                             Non-Exact

N1-ODE for p(x)                                       N1-ODE p.24-1                       Other methods:  analytical, numerical

p. 24-1

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Nth order p.24-1 Ln-ODE-VC special L2-ODE-VC Legendre Bessel, Laguerre, Hermite, etc. L2-ODE-VC Non-exact Inverse method: Start w/ solution  Other methods analytical Transformation of variable Trial solution (undetermined coeff.) Single Term                              Polynomial Series:  Frobenius $$x^c e^{rx}$$                                             $$x^c \sum d_i x^i$$