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## Homework Statement

Verify that the given function is in the kernel of L.

y(x)=x

^{-2}

L = x

^{2}D

^{2}+ 2xD - 2

## Homework Equations

## The Attempt at a Solution

I took the first and 2nd derivative of y(x), and got

y

^{'}(x)= -2x

^{-3}

y

^{''}(x)= 6x

^{-4}

Then plugged it into L (and a little simplifying) and got

L(y) = 6x

^{-2}+2x

^{-1}-2

I think I'm supposed to plug it in, and verify that it's equal to zero, but it's not coming out right.

Any obvious mistakes? Or wrong direction all together?