Answer
0; $y(x)=x^{-2} \in ker(L)$
Work Step by Step
We have: $Ly=x^2D^2+2xD-2$
$L(x^{-2})=x^2(6e^{-4})+2x(-2x^{-3}-2x^{-2}\\=6x^{-2}-4x^{-2}-2x^{-2}\\=0$
This yields $y(x)=x^{-2} \in ker(L)$
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: 6
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