Answer
See below
Work Step by Step
Given:$$y'''+x^2y''-(\sin x)y'+e^xy=x^3$$
Rewrite: $$[D^3y+x^2D^2-\sin x)D+e^x][y]=x^3$$
The associated homogeneous differential equation: $$y'''+x^2y''-(\sin x)y'+e^xy=0$$
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: 17
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