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Unformatted text preview: 98 1 Solutions 30.
31.
, 32. , , 33. The initial condition occurs at
which is precisely where
has a zero. Theorem 6 does not apply.
34. In this case
and
. The function
,
is a
solution to the initial value problem. By the uniqueness part of Theorem
6
is the only solution.
35. The assumptions say that
and
. Both
and
therefore satisﬁes the same initial conditions. By the uniqueness
part of Theorem 6
. Section 4.2
1. dependent; and are multiples of each other. 2. independent
3. independent
4. dependent;
other. and , they are multiples of each 5. independent
6. dependent; and 7. dependent; , they are multiples of each other.
, they are multiples of each other. 8. dependent;
multiples of each other.
9. 1. Suppose
get and
on These equations imply
dent.
2. Observe that
then , they are
. Then for . So and and are linearly indepenif
if and
. If we then If ...
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This note was uploaded on 12/22/2011 for the course MAP 2302 taught by Professor Bell,d during the Fall '08 term at UNF.
 Fall '08
 BELL,D

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