(cos r- sin r) is a particular solution to y" – 3y' +2y = e" sin x = x2 + 3x + 3 is a particular solution to y" – 3y + 2y = 2x?. Find a Suppose that Yı and that y2 particular solution to each of the following: (a) y" – 3y' + 2y = 3e" sin r + 8a? (b) y" – 3y' + 2y = 4x2 – 6e" sin r

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Suppose that \( y_1 = \frac{e^x}{2} (\cos x - \sin x) \) is a particular solution to \( y'' - 3y' + 2y = e^x \sin x \) and that \( y_2 = x^2 + 3x + \frac{7}{2} \) is a particular solution to \( y'' - 3y' + 2y = 2x^2 \). Find a particular solution to each of the following:

(a) \( y'' - 3y' + 2y = 3e^x \sin x + 8x^2 \)

(b) \( y'' - 3y' + 2y = 4x^2 - 6e^x \sin x \)
Transcribed Image Text:Suppose that \( y_1 = \frac{e^x}{2} (\cos x - \sin x) \) is a particular solution to \( y'' - 3y' + 2y = e^x \sin x \) and that \( y_2 = x^2 + 3x + \frac{7}{2} \) is a particular solution to \( y'' - 3y' + 2y = 2x^2 \). Find a particular solution to each of the following: (a) \( y'' - 3y' + 2y = 3e^x \sin x + 8x^2 \) (b) \( y'' - 3y' + 2y = 4x^2 - 6e^x \sin x \)
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