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28. y" – 3y" – y' + 3y = x'e*. x²e*. %3D

28. y" – 3y" – y' + 3y = x'e*. x²e*. %3D

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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solve the question 28 within 10 mins or else downvote
23. Find the general solution of x (* - 2)y" - (x? - 2)y' + 2(x - 1)y = 3x (x - 2)e", | given that y = e* and y responding homogeneous equation. = x? are linearly independent solutions of the cor- 24. Find the general solution of (2x + 1)(x + 1)y" + 2xy' 2y = (2x + 1), given that y = x and y = (x + 1)-1 are linearly independent solutions of the corresponding homogeneous equation. 25. Find the general solution of (sin? x)y" – (2 sin x cos x)y' + (cos? x + 1)y sin x, given that y = sin x and y = x sin x are linearly independent solutions of the corresponding homogeneous equation. 26. Find the general solution of 2e* ху" — (2х + 1)y' + (x + 1)y = x? given that corresponding homogeneous equation. = e* and y x'e* are linearly independent solutions of the In each of Exercises 27 and 28, find the general solution by two methods: 27. у" — 2у 8xe2x. 28. у" — Зу" — у' + 3у %3 х*е".
Transcribed Image Text:23. Find the general solution of x (* - 2)y" - (x? - 2)y' + 2(x - 1)y = 3x (x - 2)e", | given that y = e* and y responding homogeneous equation. = x? are linearly independent solutions of the cor- 24. Find the general solution of (2x + 1)(x + 1)y" + 2xy' 2y = (2x + 1), given that y = x and y = (x + 1)-1 are linearly independent solutions of the corresponding homogeneous equation. 25. Find the general solution of (sin? x)y" – (2 sin x cos x)y' + (cos? x + 1)y sin x, given that y = sin x and y = x sin x are linearly independent solutions of the corresponding homogeneous equation. 26. Find the general solution of 2e* ху" — (2х + 1)y' + (x + 1)y = x? given that corresponding homogeneous equation. = e* and y x'e* are linearly independent solutions of the In each of Exercises 27 and 28, find the general solution by two methods: 27. у" — 2у 8xe2x. 28. у" — Зу" — у' + 3у %3 х*е".
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