Mathematics 38
Differential Equations
Examination 1
February 11, 2008
No calculators, notes, or books are allowed. Please make sure all electronic devices you carry are turned off and put
away out of sight.
Remember to sign your blue book.
With your signature you are pledging that you have neither given nor received
assistance on this exam. Good luck!
1.
(3 points each, no partial credit) For each of the differential equations below determine the order, determine whether
the differential equation is linear, and if so, whether it is homogeneous.
a.
t
4
d
3
x
dt
3
+
t
dx
dt

t

x
7
= 0
b.
dx
dt
+
d
7
x
dt
7
=
x
+
t
9
c.
(
dx
dt
)
5
+
d
4
x
dt
4

t
3
x
+
t
7
= 0
d.
x
′
x
′′′
=
x
4
x
′′
+
t
5
x
′
2.
(3 points each, no partial credit) Find all real values of
α
for which the given function is a solution of the given
differential equation.
a.
x
=
α
,
d
7
x
dt
7
+ sin
t
dx
dt
+
x

4 = 0
b.
x
=
α
t
2
+ 1
,
dx
dt
+ 2
tx
2
= 0
c.
x
=
e
αt
,
xx
′
=
e
2
t
3.
(1 point each) For each of the following differential equations state whether it is normal on
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 Fall '08
 any
 Differential Equations, Equations, Derivative, dt dt dx

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