Question

Find L1L2 and L2L1 for the given differential operators and determine whether L1L2= L2L1
L1= D +1
L2= D - 2x^2
Please, help

Answer 1

@primeralph

Answer 2

Just check if they commute.

Answer 3

how?

Answer 4

I got it wrong, since L1 = D +1 so L1 = y' +y
and L2= D -2x^2 = y' - 2x^2 y
L1L2 = (y'+y)((y' +2x^2 y)
is it right?

Answer 5

and then L2L1 are the same, but the answer in the back of the book said that they are not equal :(

Answer 6

L1L2 means you apply the operation on L2; so that's L2' +L2.
So for L1L2y = L1(y'-2x^2 y) = (y'-2x^2 y)' + (y'-2x^2 y)

Answer 7

Commuting means L1L2 - L2L1 = 0.

Answer 8

so?

Answer 9

So read what I wrote.

Answer 10

L2'+L2 for L1L2, right?
L1' -2x^2L1 for L2L1, right?

Answer 11

Then you have to apply them on some function and see if they are the same.

Answer 12

got you, thanks a lot

Answer 13

You're welcome.