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Prof.
S.L.
Phoenix
9/06/11
TAM 3100
Method of Undermined Coefficients: Two Useful Rules and a Table
Rule 1:
In solving
Ly
f x
suppose that no term appearing either in
fx
or in any of its
derivatives satisfies the homogeneous equation
0
.
Then take as a trial solution for
p
y
a
linear combination of all linearly independent such terms in
and their derivatives.
Then
determine the coefficients by substitution of this trial solution into the nonhomogeneous
equation,
.
If this works, then you are fine.
Rule 2:
If the function
is of the form
cos
or
sin
rx
rx
mm
Pxe
k
x
k
x
(
1
)
where
m
Px
is a polynomial in
x
of degree
m
, then take as a trial solution of the form
2
01
2
2
2
...
cos
...
sin
sm
r
x
pm
mr
x
m
yx x A A
xA
x
A
xe
k
x
BB
x
B
x
B
x
e
k
x
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This note was uploaded on 09/29/2011 for the course TAM 310 at Cornell University (Engineering School).
 '08
 PHOENIX

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