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

Name: please help for # 26 **Problem Set: Particular Solutions**In Problems
Uploaded: 2024-03-20T06:46:03.000Z
Channel: Bartleby
Description: 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.**