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

Calculus: Early Transcendentals
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ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
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Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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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
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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