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c) y" - 4y + 3y = e³t

c) y" - 4y + 3y = e³t

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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The image contains differential equations labeled as c) and d), presented as follows: **c) \( y'' - 4y' + 3y = e^{3t} \)** This equation represents a second-order linear non-homogeneous differential equation where \( y'' \) is the second derivative of \( y \) with respect to \( t \), \( y' \) is the first derivative, and \( y \) is the function of \( t \). The non-homogeneous part of the equation is given by \( e^{3t} \). **d) \( y'' - 6y' + 9y = e^{3t} \)** Similarly, this is another second-order linear non-homogeneous differential equation where \( y'' \) is the second derivative of \( y \) with respect to \( t \), \( y' \) is the first derivative, and \( y \) is the function of \( t \). The non-homogeneous part of the equation is also given by \( e^{3t} \). In both equations, the goal is to find the function \( y(t) \) that satisfies these differential equations.
Transcribed Image Text:The image contains differential equations labeled as c) and d), presented as follows: **c) \( y'' - 4y' + 3y = e^{3t} \)** This equation represents a second-order linear non-homogeneous differential equation where \( y'' \) is the second derivative of \( y \) with respect to \( t \), \( y' \) is the first derivative, and \( y \) is the function of \( t \). The non-homogeneous part of the equation is given by \( e^{3t} \). **d) \( y'' - 6y' + 9y = e^{3t} \)** Similarly, this is another second-order linear non-homogeneous differential equation where \( y'' \) is the second derivative of \( y \) with respect to \( t \), \( y' \) is the first derivative, and \( y \) is the function of \( t \). The non-homogeneous part of the equation is also given by \( e^{3t} \). In both equations, the goal is to find the function \( y(t) \) that satisfies these differential equations.
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