Differential Equations Exam Review (1 of 6) - Review 5:...

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Review 5: L29-L32
1. Solve the initial value problem by using the Laplace transform:
(a)
2 y y y t
′′ ′
− + =
,
( ) ( )
0 0, 0 1 y y
′
(b) cos2 w w t
′′+
=
0
2
w
π
 
=
 
 
,
1
2
w
π
 
′ =
 

=

=
2. (a) Sketch the graph of the piecewise continuous function and express it in terms of
the unit step function.
(b) Find L
( )
{ }
( )
f t s .
3. Find the following transforms:
4
3 2
4. (a) Represent
( )
g t in terms of the unit step functions and determine L
( )
{ }
g t
(b) Use part (a) to solve the initial value problem:
5. (a) Represent
( )
g t in terms of the unit step functions and determine L
( )
{ }
g t :
(b) Use part (a) to solve the initial value problem:
.

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