MATH 315 FALL 2006 TEST 3 SOLUTION KEY
Note: the following solutions are for one version of the test; some final solutions for the
alternate test version problems are also given.
1.
(20 pts.) Use Power series to solve the differential equation
with
.
1.
Find the recursion formula for the coefficients
in the power series
representation of the solution
.
Answer:
,
so
,
(
alternate
test version
,
),
and
, or
for
.
2.
Determine the first
six
terms in the series for
.
Answer:
using intial value
, then
,
;
final solution
:
(
alternate
test version
).
2.
(22 pts.) Use Laplace transforms to solve
with
,
.
Answer:
the transformed equation becomes
or

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, and therefore
. Using partial fractions
, so
, or
,
and therefore
,
,
, so
and
.
Then
;
final solution
:
(
alternate
test version
).
3.
(13 pts.) Find the Laplace transform