26. y'"-8y +16y = 6xe4x + 2 + 16x + 16x²

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
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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In Exercises 24–29, use the principle of superposition to find a particular solution.

24. \( y'' + y' + y = xe^x + e^{-x}(1 + 2x) \)

25. \( y'' - 7y' + 12y = -e^x(17 - 42x) - e^{3x} \)

26. \( y'' - 8y' + 16y = 6xe^{4x} + 2 + 16x + 16x^2 \)

27. \( y'' - 3y' + 2y = -e^{2x}(3 + 4x) - e^x \)

28. \( y'' - 2y' + 2y = e^x(1 + x) + e^{-x}(2 - 8x + 5x^2) \)
Transcribed Image Text:In Exercises 24–29, use the principle of superposition to find a particular solution. 24. \( y'' + y' + y = xe^x + e^{-x}(1 + 2x) \) 25. \( y'' - 7y' + 12y = -e^x(17 - 42x) - e^{3x} \) 26. \( y'' - 8y' + 16y = 6xe^{4x} + 2 + 16x + 16x^2 \) 27. \( y'' - 3y' + 2y = -e^{2x}(3 + 4x) - e^x \) 28. \( y'' - 2y' + 2y = e^x(1 + x) + e^{-x}(2 - 8x + 5x^2) \)
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