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Math 303 Review Sheet 2 Chapters 34
1. A. Solve the following linear diﬀerential equations
y
00

y
= 0
with y
(0) = 3
,y
0
(0) = 1.
B. First solve the following linear diﬀerential equations 9
y
00
+ 3
y
0

2
y
= 0
,with y
(0) = 9
,y
0
(0) =

3, then describe
the behavior the of solution.
C. If
y
(
t
) is the solution of
y
00
+3
y
0
+2
y
= 0 with
y
(0) = 10 and
y
0
(0) =

20, then what is the limit of
y
(
t
) as
t
→ ∞
?
2.A. Determine the longest interval in which the given initial value problem is certain to have a unique twice dif
ferentiable solution.
(a) (
x

4)
y
00
+ 2
xy
0
+ (
sinx
)
y
= 0
with y
(0) = 1
and y
0
(0) = 2
(b) (
t
2

4)
y
00
+
ln
(
t
+ 5)
y
0

(
t
+ 2)
y
= 0
with y
(3) = 2
and y
0
(3) =

4.
B. Find two real solutions
y
1
(
x
),
y
2
(
x
) of equation (
y
0
)
3
y
00

y
3
= 0 and check that
c
1
y
1
(
x
)+
c
2
y
2
(
x
) is also a solution.
3. Determine whether a pair of functions are linearly dependent or linearly independent.
A.
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This note was uploaded on 11/29/2011 for the course MATH 303 taught by Professor Anderson,m during the Winter '08 term at BYU.
 Winter '08
 Anderson,M
 Math, Equations

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