Chapter 4
11.
The answer is “no”, because the method of undetermined coeﬃcients cannot be applied to
y
0
−
6
y
0
−
4
y
=
1
t
.
13.
In the original form, the function sin
2
t
does not Ft any of the cases in the method of unde
termined coeﬃcients. But it can be written as sin
2
t
=(1
−
cos 2
t
)
/
2, and so
2
t
+sin
2
t
+3=2
t
+
1
−
cos 2
t
2
+3=
±
2
t
+
7
2
²
−
±
1
2
cos 2
t
²
.
Now, the method of undetermined coeﬃcients can be applied to each term in the above
di±erence to Fnd a particular solution to the corresponding nonhomogeneous equation, and
the di±erence of these particular solutions, by the superposition principle, is a particular
solution to the original equation. Thus, the answer is “yes”.
15.
“No”, because the given equation is not an equation with constant coeﬃcients.
17.
The auxiliary equation in this problem is
r
2
−
1=0w
ithroots
r
=
±
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 Spring '10
 Hald,OH
 Math, Differential Equations, Linear Algebra, Algebra, Equations, undetermined coefficients

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