MATH 3200
Review for Test 1
Bennethum
These are practice problems for test 1. For this exam, one side of an 8.5x11” sheet of
paper will be allowed for notes. No technology of any kind will be allowed. The topics covered
on this exam include material covered in Chapters 1 and 2. Long application problems will
not be on the exam (this is why you have a project due). Answers are given on the last page.
1. Classify the following ODE. Determine the order, whether it is linear or nonlinear,
whether it is autonomous, and if linear, whether it is homogeneous. Circle all that are
correct.
(a)
t
4
y
′
+
y
sin(
t
) = 6
A) firstorder, secondorder, thirdorder
B) linear, nonlinear
C) homogeneous, nonhomogeneous
D) autonomous, nonautonomous
(b)
yy
′′
=
x
3
+
y
sin(3
x
)
A) firstorder, secondorder, thirdorder
B) linear, nonlinear
C) homogeneous, nonhomogeneous
D) autonomous, nonautonomous
(c) (
y
′
)
3
+
t
5
sin
y
=
y
4
A) firstorder, secondorder, thirdorder
B) linear, nonlinear
C) homogeneous, nonhomogeneous
D) autonomous, nonautonomous
(d)
y
′
(
x
2
+ 1)
y
= cos
x
A) firstorder, secondorder, thirdorder
B) linear, nonlinear
C) homogeneous, nonhomogeneous
D) autonomous, nonautonomous
2. Determine whether the function is a solution to the following particular problem. If
not, explain why.
(a)
y
=
x
2
y
′
=
xy
2

2
x,
y
(1) = 1
(b)
y
= 3 sin 2
t
+
e
−
t
y
′′
+ 4
y
= 5
e
−
t
,
y
(0) = 1
3. Find the general solution of the following equations.
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 Spring '06
 Bennethum
 Math, Differential Equations, Equations

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