Answer
See below
Work Step by Step
Given:$$y''+4xy'-6x^2y=x^2\sin x$$
Rewrite: $$(D^2y+4Dx-6x^2)[y]=x^3$$
The associated homogeneous differential equation: $$y''+4xy'-6x^2y=0$$
Differential Equations and Linear Algebra (4th Edition)
by Goode, Stephen W.; Annin, Scott A.
Published by
Pearson
ISBN 10:
0-32196-467-5
ISBN 13:
978-0-32196-467-0
Chapter 8 - Linear Differential Equations of Order n - 8.1 General Theory for Linear Differential Equations - Problems - Page 503: 18
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