Sharma_MAT_275_ONLINE_B_Summer_2019.earena.Section_6.2_Solution_of_I.V.P.pdf

Elizabeth Arena Sharma MAT 275 ONLINE B Summer 2019
Assignment Section 6.2 Solution of I.V.P due 08/08/2019 at 11:59pm MST
1. (1 point)
Find the inverse Laplace transform f ( t ) =
L
- 1
{ F ( s ) } of
F ( s ) =
7 s + 3
s
y ( t ) = .
3. (1 point)
(4) Now by inverting the transform, find
y ( t ) = .
Use the Laplace transform to solve the following initial value
problem:
y
00
+ 3 y
0
- 28 y = 0 y ( 0 ) = - 2 , y
0
( 0 ) = 3
(1) First, using Y for the Laplace transform of y ( t ) , i.e.,
Y =
L
{ y ( t ) } , find the equation you get by taking the
Laplace transform of the differential equation
= 0
(2) Now solve for
Y ( s ) =
(3) Write the above answer in its partial fraction decompo-
sition, Y ( s ) =
A
s + a
+
B
s + b
where a < b
Y ( s ) = +
4. (1 point)
Use the Laplace transform to solve the following initial value
problem:
y
00
+ 5 y
0
= 0 y ( 0 ) = - 1 , y
0
( 0 ) = - 4
(1) Using Y for the Laplace transform of y ( t ) , i.e., Y =
L
{ y ( t ) } , find the equation you get by taking the
Laplace transform of the differential equation
= 0
(2) Now solve for
Y ( s ) =
(3) Write the above answer in its partial fraction decompo-
sition, Y ( s ) =
A
s + a
+
B
s + b
where a < b
Y ( s ) = +
1

(4) Now by inverting the transform, find
y ( t ) = .