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Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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Question
![According to the method of undetermined coefficients, the differential equation
y" + 4 y′ + 4y = 3 t² + (t + 2) e−2t will have a particular solution in the
form
y'
○ Yp = C₁ t² + C₂t + C3 + (C₁t + C5) e−2t
Ур
Ур
=
C₁t² + C₂t + C3 + ( C 4 t³ + C 5 t²) e−2t
Ур
=
C₁ t² + C₂ t + С3 + (C4 t + C5) 6
-2t
e
Ур
=
C₁t² + (C₂ t² + C3 t) e¯
-2t
е
Yp = C₁ t² + C₂t + C3 + (C₁ t² + C5 t) e¯
-2t
е](https://content.bartleby.com/qna-images/question/f279f7d6-c7a9-41cc-a142-21ae3817760c/f4646f9b-ed54-405f-ba0b-0b9f3b6e6810/s6fwjt9_thumbnail.png)
Transcribed Image Text:According to the method of undetermined coefficients, the differential equation
y" + 4 y′ + 4y = 3 t² + (t + 2) e−2t will have a particular solution in the
form
y'
○ Yp = C₁ t² + C₂t + C3 + (C₁t + C5) e−2t
Ур
Ур
=
C₁t² + C₂t + C3 + ( C 4 t³ + C 5 t²) e−2t
Ур
=
C₁ t² + C₂ t + С3 + (C4 t + C5) 6
-2t
e
Ур
=
C₁t² + (C₂ t² + C3 t) e¯
-2t
е
Yp = C₁ t² + C₂t + C3 + (C₁ t² + C5 t) e¯
-2t
е
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