Liner differentials of order n, Kernel

  • Thread starter bakin
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  • #1
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Homework Statement



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

y(x)=x-2
L = x2D2 + 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?
 

Answers and Replies

  • #2
Dick
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How does 2xDy become 2x^(-1)?? And the -2 isn't just a -2. L is operating on y. What should it be?
 
  • #3
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Bah, forgot about the -2 part. It's actually -2y, correct? So the last term would be -2y, or -2x-2.

And as I was typing out how I came up with 2xD, I realized I substituted just y into D, and not y' :blushing:

With the correct substitutions, I came up with:

L = x2*6x-2 + 2x*-2x-3 - 2x-2

= 6x-2 - 4x-2 - 2x-2

= 0


:tongue: Once again, thanks Dick.
 

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