find a particular solution of the given nonhomogeneous equation. a?y" + xy' + (x² – 0.25) y = 3.x/? sin r, x > 0; Y1(x) = x/2 sin x, y2(x) = x -1/2 COS x
find a particular solution of the given nonhomogeneous equation. a?y" + xy' + (x² – 0.25) y = 3.x/? sin r, x > 0; Y1(x) = x/2 sin x, y2(x) = x -1/2 COS x
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![To find a particular solution of the given nonhomogeneous equation:
\[ x^2 y'' + xy' + (x^2 - 0.25) y = 3x^{3/2} \sin x, \quad x > 0; \]
Given solutions for the corresponding homogeneous equation are:
\[ y_1(x) = x^{-1/2} \sin x, \quad y_2(x) = x^{-1/2} \cos x \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F88e1e2e4-888b-4182-8c02-fd46dda7f6b1%2Fe0d9924b-c393-45b4-8360-b44d5cbe6705%2Fnx1xxzq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:To find a particular solution of the given nonhomogeneous equation:
\[ x^2 y'' + xy' + (x^2 - 0.25) y = 3x^{3/2} \sin x, \quad x > 0; \]
Given solutions for the corresponding homogeneous equation are:
\[ y_1(x) = x^{-1/2} \sin x, \quad y_2(x) = x^{-1/2} \cos x \]
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