This preview shows page 1. Sign up to view the full content.
Unformatted text preview: 98 1 Solutions 30.
, 32. , , 33. The initial condition occurs at
which is precisely where
has a zero. Theorem 6 does not apply.
34. In this case
. The function
solution to the initial value problem. By the uniqueness part of Theorem
is the only solution.
35. The assumptions say that
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
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
on These equations imply
2. Observe that
then , they are
. Then for . So and and are linearly indepenif
. If we then If ...
View Full Document
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