Answer
$y (x)= x e^x \in ker (L)$
Work Step by Step
We have: $Ly=(-D^2+2D-1)(x e^x)$
$L(x e^x)=(-2 e^x+x e^x)+2(e^ x+x e^x)-x e^x\\=-2e^x-x e^x+2 e^x+2x e^x-x e^x \\=0$
This yields $y (x)= x e^x \in ker (L)$
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: 9
Update this answer!
You can help us out by revising, improving and updating this answer.
Update this answerAfter you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.
