MAP2302 Final
1. Given the equation 5
y
00
(
t
)

y
0
(
t
)+7
y
(
t
) = 3
te
4
t
cos 2
t
+
t
2
e
t
+4
t
3
e
2
t
sin 4
t

(2
/
3)
e
t
+9
e
2
t
cos 4
t
,
if the Method of Undetermined Coeﬃcients and the Principle of Superposition are used to ﬁnd a
particular solution, what is the minimum number of nonhomogeneous equations which must be
solved:
A. two
B. three
C. four
D. ﬁve
E. six
2. A given second order, linear, nonhomogeneous equation with constant coeﬃcients has two
linearly independent solutions
y
1
(
t
) =
e
2
t
and
y
2
(
t
) =
e

t
to the accompanying homogeneous equa
tion; if
A
= 1 and the nonhomogeneous term is given by
f
(
t
) = 6
e
4
t
, the method of variation of
parameters gives a general solution as:
A.
y
g
(
t
) =
c
1
e

t
+
c
2
e
2
t
+
e
4
t
B.
y
g
(
t
) =
c
1
e

t
+
c
2
e
2
t
+(3
/
5)
e
4
t
C.
y
g
(
t
) =
c
1
e

t
+
c
2
e
2
t
+(2
/
5)
e
4
t
D.
y
g
(
t
) =
c
1
e

t
+
c
2
e
2
t
+
te
4
t
+ (2
/
5)
e
4
t
E.
y
g
(
t
) =
c
1
e

t
+
c
2
e
2
t
+
te
3
t
+ (4
/
3)
e
4
t
3. Given the IVP 2
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 Spring '08
 TUNCER
 Cos, A., Natural logarithm, Homogeneity

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