EGM6321 - Principles of Engineering Analysis 1, Fall 2009
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Mtg 19: Tues, 5Oct09
HW: Legendre differential Eq.(1) P.14-2 with
, such that homogeneous solution
.
Use reduction of order method 2 (undetermined factor) to find
, second homgenous solution
HW: K. p28, pb. 1.1.b.
Variation of parameters (continued) P.18-4
Use expression for
Eq.(2) P.18-4 and
Eq.(3) P.18-4 in non-homogeneous L2_ODE_VC Eq.(1) P.3-1
|
(1)
|
Where
, because
is a homogeneous solution
Where
, because
is a homogeneous solution
2 equations Eq.(1) P.18-4 and Eq.(1) P.19-1 for two unknowns
In matrix form:
Where
is the Wronskian matrix designated as
The Wronskian, W, is the determinant of
If
, then
exists and
Theorem:
(function of x) are linearly independant if
, where
zero function.
|
(1)
|
|
(2)
|
Where
are known
|
(3)
|
Where
|
(4)
|
Where