• Support PF! Buy your school textbooks, materials and every day products Here!

Liner differentials of order n, Kernel

  • Thread starter bakin
  • Start date
  • #1
58
0

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
Science Advisor
Homework Helper
26,258
618
How does 2xDy become 2x^(-1)?? And the -2 isn't just a -2. L is operating on y. What should it be?
 
  • #3
58
0
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.
 

Related Threads for: Liner differentials of order n, Kernel

Replies
1
Views
2K
  • Last Post
Replies
1
Views
784
Replies
2
Views
575
Replies
1
Views
1K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
15
Views
2K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
1
Views
2K
Top