26. y" – 6y' + 13y = xe3* sin 2x |

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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please help for # 26

**Problem Set: Particular Solutions**

In Problems 21 through 30, set up the appropriate form of a particular solution \( y_p \), but do not determine the values of the coefficients.

**21.** \( y'' - 2y' + 2y = e^x \sin x \)

**22.** \( y^{(5)} - y^{(3)} = e^x + 2x^2 - 5 \)

**23.** \( y'' + 4y = 3x \cos 2x \)

**24.** \( y^{(3)} - y'' - 12y' = x - 2xe^{-3x} \)

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

**26.** \( y'' - 6y' + 13y = xe^{3x} \sin 2x \)

**27.** \( y^{(4)} + 5y'' + 4y = \sin x + \cos 2x \)

**28.** \( y^{(4)} + 9y'' = (x^2 + 1) \sin 3x \)

**29.** \( (D - 1)^3 (D^2 - 4)y = xe^x + e^{2x} + e^{-2x} \)

**30.** \( y^{(4)} - 2y'' + y = x^2 \cos x \)

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**Note:** The instructions involve finding the appropriate structure of the particular solution \( y_p \) for each differential equation, focusing on the non-homogeneous part without computing the specific coefficients involved.
Transcribed Image Text:**Problem Set: Particular Solutions** In Problems 21 through 30, set up the appropriate form of a particular solution \( y_p \), but do not determine the values of the coefficients. **21.** \( y'' - 2y' + 2y = e^x \sin x \) **22.** \( y^{(5)} - y^{(3)} = e^x + 2x^2 - 5 \) **23.** \( y'' + 4y = 3x \cos 2x \) **24.** \( y^{(3)} - y'' - 12y' = x - 2xe^{-3x} \) **25.** \( y'' + 3y' + 2y = x(e^{-x} - e^{-2x}) \) **26.** \( y'' - 6y' + 13y = xe^{3x} \sin 2x \) **27.** \( y^{(4)} + 5y'' + 4y = \sin x + \cos 2x \) **28.** \( y^{(4)} + 9y'' = (x^2 + 1) \sin 3x \) **29.** \( (D - 1)^3 (D^2 - 4)y = xe^x + e^{2x} + e^{-2x} \) **30.** \( y^{(4)} - 2y'' + y = x^2 \cos x \) --- **Note:** The instructions involve finding the appropriate structure of the particular solution \( y_p \) for each differential equation, focusing on the non-homogeneous part without computing the specific coefficients involved.
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