02
L2 44 a2
03
L3 24
04
L4 /22 X4 -
-X
a2
-2045 +/
+ (/25 + 346)
a4
- 2026 aa +
6x306y
02
355 O2'
a3
9X2ay
03 03
(314 + 356) +/315 3
04
(2312 + 066) 2ay2
a4 a4
S..2816 + 811a4
(A .',)
Now the general solution of the system of equations can be written as
L4F+ L ,'
L3F+L L,'.
(A :)
In the presence of body forces,
F F'+ Fo
(A .:)
From the above two equations,
(L4L2 L )F' = 0
(A.31)
The above sixth order operator can be broken into linear operators as,
D6DsD4DAD2DIF'
(A.32)
Where
Dx = lik-
6x 6x
(A.33)
and Pk are the roots of the equation which corresponds to the differential
equation
(A.34)
Where
b i + ,,
14 ()12 ( L) 3()