HW #11
Due: 12/04/2023
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Template
(Word file)
One page for each problem (a total of 2 pages). 50 % Penalty if not followed.
Make a single PDF file. File name:
hw_11_doe_john.pdf
.
Email the PDF file to
me5331exam@gmail.com
with the subject line:
Doe, John, HW#1
1.
Solve the following set of simultaneous differential equations for
x
(
t
),
y
(
t
) and
z
(
t
) using the Laplace transforms.
dx
dt
+
y
+
z
=
0,
(1)
x
+
dy
dt
+
z
=
0,
(2)
x
−
y
−
dz
dt
=
0,
(3)
with
x
(0) = 1,
y
(0) = 0,
z
(0) = 1.
2.
Solve the following integro-differential equation by the Laplace transform:
u
′(
t
) +
u
(
t
) +
⌠
⌡
t
0
u
(
t
− τ)
e
τ
d
τ =
e
t
− 1
with
u
(0) = 0.
File translated from T
E
X by
T
T
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, version 4.03.
On 26 Nov 2023, 08:30.
