24. Find the general solution of (2x + 1)(x + 1)y" + 2xy' – 2y = (2x + 1)², given that y = x and y = (x + 1)-1 are linearly independent solutions of the corresponding homogeneous equation.
24. Find the general solution of (2x + 1)(x + 1)y" + 2xy' – 2y = (2x + 1)², given that y = x and y = (x + 1)-1 are linearly independent solutions of the corresponding homogeneous equation.
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 24 within 10 mins or else downvote
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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