Math2306 Review Problems for Exam 3
(Covers sections 4.6, 4.8, 5.1)
1. Solve each differential equation by variation of parameters.
a)
xyy
2
cos
xxcxc
2
21
sin
3
1
3
1
sincos
b)
2/
4
x
xeyy
2/2/22/
2
2/
1
4
1
8
1
xxxx
eexecec
c)
xyy
3
sec
xxcxc sec
2
1
sincos
21
d)
xxyy sin
xxecec
xx
sin
2
1
21
2. Solve the given system of differential equations by systematic elimination.
a)
x
dt
dy
y
dt
dx
2
3
tt
tt
ececty
ecectx
6
2
6
1
6
2
6
1
3
6
3
6
)(
)(
b)
yx
dt
dy
yx
dt
dx
2
74
tt
tt
ececty
ecectx
3
2
5
1
3
2
5
1
7
1
)(
)(
c)
32
122
y
dt
dy
dt
dx
yx
dt
dy
dt
dx
3)(
2
5
2
3
)(
2
2
1
2
2
1
tt
tt
ececty
ecectx
d)
2)3()3(
2
yDxD
tDyxD
23
321
23
321
2
1
3)(
2
1
)(
ttececcty
ttececctx
tt
tt
3. Solve the given initial-value problem.
a)
1)1(,0)1(
4
5
yx
yx
dt
dy
yx
dt
dx
3333
3333
2
tt
tt
teey
teex
b)
0)0(,0)0(
23
1
yx
yx
dt
dy
y
dt
dx
1)2sin
2
2
2cos(
3
2
)2sin
6
2
2cos
3
2
(
ttey
ttex
t
t
4. A 12-pound weight stretched a spring 2 feet. The weight is released from a point 1
foot below the equilibrium position with an upward velocity of 4 ft/s. Find the
equation of motion.
4
3
4sin(24sin4cos
tttx
1
