Use the Laplace transform to solve the given initial value problem. y" + 4y' + 13y = e=2# sin3t, y(0) = 3, y (0) = – 2 25 gle cos(31) -2t y = 3e-" cos3t +e-" sin3t -te 18 -2t 18 3 25 y 19 'cos(3t) + 'sin(3t) -e 18 25 1 y = 3e-"cos3t +e 18 sin3t 'cos(3t) -te 25 Py = 3e-2 cos3t + 18 1 'cos(3t) sin3t |
Use the Laplace transform to solve the given initial value problem. y" + 4y' + 13y = e=2# sin3t, y(0) = 3, y (0) = – 2 25 gle cos(31) -2t y = 3e-" cos3t +e-" sin3t -te 18 -2t 18 3 25 y 19 'cos(3t) + 'sin(3t) -e 18 25 1 y = 3e-"cos3t +e 18 sin3t 'cos(3t) -te 25 Py = 3e-2 cos3t + 18 1 'cos(3t) sin3t |
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.2: Trigonometric Equations
Problem 104E
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Question
![Use the Laplace transform to solve the given initial value problem.
y" + 4y' + 13y = e-2# sin3t, y(0) = 3,
y (0) =
2
°y = 3e-2 cos3t +
25
-2t
-e
1
-2º cos(3t)
sin3t –
-te
%3D
18
18
3
25
-2t cos(3t) +
-2ª sin(3t)
18
y =
-e
19
25
-2' sin3t – ÷te-"cos(3t)
18
1
y = 3e-cos3t +e
y = 3e-"cos3t +e-" sin3t - że
25
-2t
1
cos(3t)
-2t
18](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc3394273-72c7-4098-9246-650448d9c593%2Fdda79c73-cf7e-440d-85d9-8b1e8e030349%2Fig6mdto_processed.png&w=3840&q=75)
Transcribed Image Text:Use the Laplace transform to solve the given initial value problem.
y" + 4y' + 13y = e-2# sin3t, y(0) = 3,
y (0) =
2
°y = 3e-2 cos3t +
25
-2t
-e
1
-2º cos(3t)
sin3t –
-te
%3D
18
18
3
25
-2t cos(3t) +
-2ª sin(3t)
18
y =
-e
19
25
-2' sin3t – ÷te-"cos(3t)
18
1
y = 3e-cos3t +e
y = 3e-"cos3t +e-" sin3t - że
25
-2t
1
cos(3t)
-2t
18
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